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Hypothesis Testing Calculator

Understanding Hypothesis Testing: A Guide to the Hypothesis Testing Calculator

Hypothesis testing is a crucial statistical method used to make informed decisions about data and draw conclusions. Whether you’re a student, researcher, or professional, a Hypothesis Testing Calculator can be an invaluable tool in your statistical toolkit. Let’s explore what hypothesis testing is and how this calculator can assist you:

Hypothesis Testing Basics:

  • Null Hypothesis (H0): This is the default assumption or claim that there is no significant difference or effect. It’s often denoted as H0.
  • Alternative Hypothesis (Ha): This is the statement that contradicts the null hypothesis. It suggests that there is a significant difference or effect. It’s denoted as Ha.
  • Significance Level (α): This is the predetermined threshold (e.g., 0.05 or 5%) used to determine statistical significance. If the calculated p-value is less than α, you reject the null hypothesis.
  • p-value: This is the probability of observing the results (or more extreme results) if the null hypothesis is true. A small p-value suggests that the results are unlikely under the null hypothesis.

Key Features of the Hypothesis Testing Calculator:

  • Input Parameters: The calculator typically requires you to input sample data, choose the type of test (e.g., t-test, chi-square test), specify the null and alternative hypotheses, and set the significance level.
  • Calculations: Once you input the data and parameters, the calculator performs the necessary statistical tests and calculations. It generates results such as the test statistic, degrees of freedom, and the p-value.
  • Interpretation: Based on the results, the calculator helps you determine whether to reject or fail to reject the null hypothesis. It provides an interpretation of the findings, which is crucial for drawing conclusions.
  • Visual Representation: Some calculators may offer visual aids like graphs or charts to help you better understand the data distribution and test results.

Significance of the Hypothesis Testing Calculator:

  • Scientific Research: Researchers across various fields use hypothesis testing to validate their hypotheses and draw meaningful conclusions from data.
  • Quality Control: Industries use hypothesis testing to ensure the quality and consistency of products and processes.
  • Medical Studies: In medical research, hypothesis testing helps assess the effectiveness of treatments or interventions.
  • Academics: Students and educators use hypothesis testing to teach and learn statistical concepts and conduct experiments.
  • Data-Driven Decisions: Businesses use hypothesis testing to make data-driven decisions, such as whether to launch a new product based on market research.

Conclusion:

The Hypothesis Testing Calculator is a powerful tool that simplifies complex statistical analysis and enables data-driven decision-making. Whether you’re conducting experiments, analyzing survey data, or performing quality control, understanding hypothesis testing and using this calculator can help you make informed choices and contribute to evidence-based research and decision-making.

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Testing a Population  Standard Deviation (data)

Input your values with a space or comma between in the table below

CRITICAL VALUES

Results shown here

SAMPLE SIZE, n

Sample standard deviation, standardized sample score, sample variance.

Section 10.4: Hypothesis Tests for a Population Standard Deviation

  • 10.1 The Language of Hypothesis Testing
  • 10.2 Hypothesis Tests for a Population Proportion
  • 10.3 Hypothesis Tests for a Population Mean
  • 10.4 Hypothesis Tests for a Population Standard Deviation
  • 10.5 Putting It Together: Which Method Do I Use?

By the end of this lesson, you will be able to...

  • test hypotheses about a population standard deviation

For a quick overview of this section, watch this short video summary:

Before we begin this section, we need a quick refresher of the Χ 2 distribution.

The Chi-Square ( Χ 2 ) distribution

Reminder: "chi-square" is pronounced "kai" as in sky, not "chai" like the tea .

If a random sample size n is obtained from a normally distributed population with mean μ and standard deviation σ , then

has a chi-square distribution with n-1 degrees of freedom.

Properties of the Χ 2 distribution

  • It is not symmetric.
  • The shape depends on the degrees of freedom.
  • As the number of degrees of freedom increases, the distribution becomes more symmetric.
  • Χ 2 ≥0

Finding Probabilities Using StatCrunch

We again have some conditions that need to be true in order to perform the test 

  • the sample was randomly selected, and
  • the population from which the sample is drawn is normally distributed

Note that in the second requirement, the population must be normally distributed. The steps in performing the hypothesis test should be familiar by now.

Performing a Hypothesis Test Regarding σ

Step 1 : State the null and alternative hypotheses.

Step 2 : Decide on a level of significance, α .

Step 4 : Determine the P -value.

Step 5 : Reject the null hypothesis if the P -value is less than the level of significance, α.

Step 6 : State the conclusion.

In Example 2 , in Section 10.2, we assumed that the standard deviation for the resting heart rates of ECC students was 12 bpm. Later, in Example 2 in Section 10.3, we considered the actual sample data below.

( Click here to view the data in a format more easily copied.)

Based on this sample, is there enough evidence to say that the standard deviation of the resting heart rates for students in this class is different from 12 bpm?

Note: Be sure to check that the conditions for performing the hypothesis test are met.

[ reveal answer ]

From the earlier examples, we know that the resting heart rates could come from a normally distributed population and there are no outliers.

Step 1 : H 0 : σ = 12 H 1 : σ ≠ 12

Step 2 : α = 0.05

Step 4 : P -value = 2P( Χ 2 > 15.89) ≈ 0.2159

Step 5 : Since P -value > α , we do not reject H 0 .

Step 6 : There is not enough evidence at the 5% level of significance to support the claim that the standard deviation of the resting heart rates for students in this class is different from 12 bpm.

Hypothesis Testing Regarding σ Using StatCrunch

Let's look at Example 1 again, and try the hypothesis test with technology.

Using DDXL:

Using StatCrunch:

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Here you can find out everything about location parameters and dispersion parameters and how you can describe and clearly present your data using characteristic values.

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Here you will find everything about hypothesis testing: One sample t-test , Unpaired t-test , Paired t-test and Chi-square test . You will also find tutorials for non-parametric statistical procedures such as the Mann-Whitney u-Test and Wilcoxon-Test . mann-whitney-u-test and the Wilcoxon test

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Levene Test

The Levene Test checks your data for variance equality. Thus, the levene test is used as a prerequisite test for many hypothesis tests .

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Standardized Test Statistic Calculator

Hypothesis Testing Calculator to find Standardized Test Statistic. This type of test is used in hypothesis testing. A standardized test is scored in a standard manner. A statistical hypothesis test is a method of statistical inference. Subtract Sample Mean by Population Mean, divide Sample Standard Deviation by Sample Size and then divide both the answer in the below Standardized Test Statistic calculator to calculate Hypothesis Test for z-scores.

Hypothesis Testing Calculator z Test

Calculate Standardized Test Statistic for a sample of 9 lightbulbs whose sample mean of the battery is 80 hours, standard deviation of 10 hours and population mean of 75 hours.

Standardized Test Statistic for z-scores = (x̄ - μ 0 ) / (σ / √n) = (80 - 75) / (10 / √9) = 1.5

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T-test for two Means – Unknown Population Standard Deviations

Instructions : Use this T-Test Calculator for two Independent Means calculator to conduct a t-test for two population means (\(\mu_1\) and \(\mu_2\)), with unknown population standard deviations. This test apply when you have two-independent samples, and the population standard deviations \(\sigma_1\) and \(\sigma_2\) and not known. Please select the null and alternative hypotheses, type the significance level, the sample means, the sample standard deviations, the sample sizes, and the results of the t-test for two independent samples will be displayed for you:

hypothesis testing calculator standard deviation

The T-test for Two Independent Samples

More about the t-test for two means so you can better interpret the output presented above: A t-test for two means with unknown population variances and two independent samples is a hypothesis test that attempts to make a claim about the population means (\(\mu_1\) and \(\mu_2\)).

More specifically, a t-test uses sample information to assess how plausible it is for the population means \(\mu_1\) and \(\mu_2\) to be equal. The test has two non-overlapping hypotheses, the null and the alternative hypothesis.

The null hypothesis is a statement about the population means, specifically the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis.

Properties of the two sample t-test

The main properties of a two sample t-test for two population means are:

  • Depending on our knowledge about the "no effect" situation, the t-test can be two-tailed, left-tailed or right-tailed
  • The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis is true
  • The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true
  • In a hypothesis tests there are two types of errors. Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis

How do you compute the t-statistic for the t test for two independent samples?

The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on whether the population variances are assumed to be equal or not. If the population variances are assumed to be unequal, then the formula is:

On the other hand, if the population variances are assumed to be equal, then the formula is:

Normally, the way of knowing whether the population variances must be assumed to be equal or unequal is by using an F-test for equality of variances.

With the above t-statistic, we can compute the corresponding p-value, which allows us to assess whether or not there is a statistically significant difference between two means.

Why is it called t-test for independent samples?

This is because the samples are not related with each other, in a way that the outcomes from one sample are unrelated from the other sample. If the samples are related (for example, you are comparing the answers of husbands and wives, or identical twins), you should use a t-test for paired samples instead .

What if the population standard deviations are known?

The main purpose of this calculator is for comparing two population mean when sigma is unknown for both populations. In case that the population standard deviations are known, then you should use instead this z-test for two means .

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9.4: Two Variance or Standard Deviation F-Test

  • Last updated
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  • Page ID 27814

  • Rachel Webb
  • Portland State University

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9.5.1 The F-Distribution

An F-distribution is another special type of distribution for a continuous random variable.

Properties of the F-distribution density curve:

  • Right skewed.
  • F-scores cannot be negative.
  • The spread of an F-distribution is determined by the degrees of freedom of the numerator , and by the degrees of freedom of the denominator . The df are usually determined by the sample sizes of the two populations or number of groups.
  • The total area under the curve is equal to 1 or 100%.

The shape of the distribution curve changes when the degrees of freedom change. Figure 9-9 shows examples of F-distributions with different degrees of freedom.

clipboard_eb66a97ca37e39efefaab6d5bd8398344.png

We will use the F-distribution in several types of hypothesis testing. For now, we are just learning how to find the critical value and probability using the F-distribution.

Use the TI-89 Distribution menu; or in Excel F.INV to find the critical values for the F-distribution for tail areas only, depending on the degrees of freedom. When finding a probability given an F-score, use the calculator Fcdf function under the DISTR menu or in Excel use F.DIST. Note that the TI-83 and TI-84 do not come with the INVF function, but you may be able to find the program online or from your instructor.

Alternatively, use the calculator at https://homepage.divms.uiowa.edu/~mbognar/applets/f.html which will also graph the distribution for you and shade in one tail at a time. You will see the shape of the F-distribution change in the following examples depending on the degrees of freedom used. For your own sketch just make sure you have a positively skewed distribution starting at zero.

The critical values F \(\alpha\) /2 and F 1–\(\alpha\)/2 are for a two-tailed test on the F-distribution curve with area 1 – \(\alpha\) between the critical values as shown in Figure 9-10. Note that the distribution starts at zero, is positively skewed, and never has negative F-scores.

clipboard_eeeaf0b38fe146f0d562669c9f4d7f2ca.png

Figure 9-10

Compute the critical values F \(\alpha\)/2 and F 1–\(\alpha\)/2 with df 1 = 6 and df 2 = 14 for a two-tailed test, \(\alpha\) = 0.05.

Start by drawing the curve and finding the area in each tail. For this case, it would be an area of \(\alpha\)/2 in each tail. Then use technology to find the F-scores. Most technology only asks for the area to the left of the F-score you are trying to find. In Excel the function for F \(\alpha\)/2 is F.INV(area in left-tail, df 1 , df 2 ).

There is only one function, so use areas 0.025 and 0.975 in the left tail. For this example, we would have critical values F 0.025 = F.INV(0.025,6,14) = 0.1888 and F 0.975 = F.INV(0.975,6,14) = 3.5014. See Figure 9-11.

clipboard_eb818775e6b57beed4b08f890cee7dc20.png

Figure 9-11

We have to calculate two distinct F-scores unlike symmetric distribution where we could just do ±z-score or ±t-score.

Note if you were doing a one-tailed test then do not divide alpha by two and use area = \(\alpha\) for a left-tailed test and area = 1 – \(\alpha\) for a right-tailed test.

Find the critical value for a right-tailed test with denominator degrees of freedom of 12 and numerator degrees of freedom of 2 with a 5% level of significance.

Draw the curve and shade in the top 5% of the upper tail since \(\alpha\) = 0.05, see Figure 9-12. When using technology, you will need the area to the left of the critical value that you are trying to find. This would be 1 – \(\alpha\) = 0.95. Then identify the degrees of freedom. The first degrees of freedom are the numerator df , therefore df 1 = 2. The second degrees of freedom are the denominator df , therefore df 2 = 12. Using Excel, we would have =F.INV(0.95,2,12) = 3.8853.

clipboard_e18eba10cbbaf44b0f1c7fb5203089abc.png

Figure 9-12

Compute P(F > 3.894), with df 1 = 3 and df 2 = 18

In Excel, use the function F.DIST(x,deg_freedom1,deg_freedom2,cumulative). Always use TRUE for the cumulative. The F.DIST function will find the probability (area) below F. Since we want the area above F we would need to also use the complement rule. The formula would be =1-F.DIST(3.894,3,18,TRUE) = 0.0263.

TI-84: The TI-84 calculator has a built in F-distribution. Press [2 nd ] [DISTR] (this is F5: DISTR in the STAT app in the TI-89), then arrow down until you get to the Fcdf and press [Enter]. Depending on your calculator, you may not get a prompt for the boundaries and df. If you just see Fcdf( then you will need to enter each the lower boundary, upper boundary, df 1 , and df 2 with a comma between each argument. The lower boundary is the 3.394 and the upper boundary is infinity (TI-83 and 84 use a really large number instead of ∞), then enter the two degrees of freedom. Press [Paste] and then [Enter], this will put the Fcdf(3.894,1E99,3,18) on your screen and then press [Enter] again to calculate the value.

clipboard_e98c6426f8577db39ad10e36147682501.png

Figure 9-13.

clipboard_ecc4ee21fb706db5ec3e8a5c662cf135b.png

Figure 9-13

9.5.2 Hypothesis Test for Two Variances

Sometimes we will need to compare the variation or standard deviation between two groups. For example, let’s say that the average delivery time for two locations of the same company is the same but we hear complaint of inconsistent delivery times for one location. We can use an F-test to see if the standard deviations for the two locations was different.

There are three types of hypothesis tests for comparing the ratio of two population variances , see Figure 9-14.

clipboard_ed1db703c4df0cff23ec4046f11dd1ccd.png

Figure 9-14

If we take the square root of the variance, we get a standard deviation. Therefore, taking the square root of both sides of the hypotheses, we can also use the same test for standard deviations. We use the following notation for the hypotheses.

There are 3 types of hypothesis tests for comparing the population standard deviations σ 1 / σ 2 , see Figure 9-15.

clipboard_eb049b72cbfb13e29521bfb93f270c305.png

Figure 9-15

The F-test is a statistical test for comparing the variances or standard deviations from two populations.

The formula for the test statistic is \(F=\frac{s_{1}^{2}}{s_{2}^{2}}\).

With numerator degrees of freedom = N df = n 1 – 1, and denominator degrees of freedom = D df = n 2 – 1.

This test may only be used when both populations are independent and normally distributed.

Important: This F-test is not robust (a statistic is called “robust” if it still performs reasonably well even when the necessary conditions are not met). In particular, this F-test demands that both populations be normally distributed even for larger sample sizes. This F-test yields unreliable results when this condition is not met.

The traditional method (or critical value method), and the p-value method are performed with steps that are identical to those when performing hypothesis tests from previous sections.

A researcher claims that IQ scores of university students vary less than (have a smaller variance than) IQ scores of community college students. Based on a sample of 28 university students, the sample standard deviation 10, and for a sample of 25 community college students, the sample standard deviation 12. Test the claim using the traditional method of hypothesis testing with a level of significance \(\alpha\) = 0.05. Assume that IQ scores are normally distributed.

1. The claim is “IQ scores of university students (Group 1) have a smaller variance than IQ scores of community college students (Group 2).”

This is a left-tailed test; therefore, the hypotheses are: \(\begin{aligned} &H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ &H_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \end{aligned}\).

2. We are using the F-test because we are performing a test about two population variances. We can use the F-test only if we assume that both populations are normally distributed. We will assume that the selection of each of the student groups was independent.

The problem gives us s 1 = 10, n 1 = 28, s 2 = 12, and n 2 = 25.

The formula for the test statistic is \(F=\frac{s_{1}^{2}}{s_{2}^{2}}=\frac{10^{2}}{12^{2}}=0.6944\).

3. The critical value for a left-tailed test with a level of significance \(\alpha\) = 0.05 is found using the invF program or Excel. See Figure 9-16.

Using Excel: The critical value is F \(\alpha\) =F.INV(0.05,27,24) = 0.5182.

clipboard_e0689195e3a35b963a5bd6c0690181e14.png

Figure 9-16

4. Decision: Compare the test statistic F = 0.6944 with the critical value F \(\alpha\) = 0.5182, see Figure 9-16. Since the test statistic is not in the rejection region, we do not reject H 0 .

5. Summary: There is not enough evidence to support the claim that the IQ scores of university students have a smaller variance than IQ scores of community college students.

A random sample of 20 graduate college students and 18 undergraduate college students indicated these results concerning the amount of time spent in volunteer service per week. At \(\alpha\) = 0.01 level of significance, is there sufficient evidence to conclude that graduate students have a higher standard deviation of the number of volunteer hours per week compared to undergraduate students? Assume that number of volunteer hours per week is normally distributed.

A researcher is studying the variability in electricity (in kilowatt hours) people from two different cities use in their homes. Random samples of 17 days in Sacramento and 16 days in Portland are given below. Test to see if there is a difference in the variance of electricity use between the two cities at α = 0.10. Assume that electricity use is normally distributed, use the p-value method.

clipboard_e9e6c1ba08d9a2d4da48e52fd3bc2ea86.png

The populations are independent and normally distributed.

The hypotheses are \(\begin{aligned} &\mathrm{H}_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ &\mathrm{H}_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{aligned}\)

Use technology to compute the standard deviations and sample sizes. Enter the Sacramento data into list 1, then do 1-Var Stats L1 and you should get s 1 = 163.2362 and n 1 = 17. Enter the Portland data into list 2, then do 1-Var Stats L2 and you should get s 2 = 179.3957 and n 2 = 16. Alternatively, use Excel’s descriptive statistics.

The test statistic is

The p-value would be double the area to the left of F = 0.82796 (Use double the area to the right if the test statistic is > 1).

clipboard_ef9a8e4c8ae93fc9217e1278519ea7848.png

Using the TI calculator Fcdf(0,0.82796,16,15).

In Excel we get the p-value =2*F.DIST(E8,E7,F7,TRUE) = 0.7106.

Since the p-value is greater than alpha, we would fail to reject H 0 .

There is no statistically significant difference between variance of electricity use between Sacramento and Portland.

Excel: When you have raw data, you can use Excel to find all this information using the Data Analysis tool. Enter the data into Excel, then choose Data > Data Analysis > F-Test: Two Sample for Variances.

clipboard_ea099e85f4800e6c40b87c2daeae9affb.png

Enter the necessary information as we did in previous sections (see below) and select OK. Note that Excel only does a one-tail F-test so use \(\alpha\)/2 = 0.10/2 = 0.05 in the Alpha box.

clipboard_ecccffce8784da391412b5e2a07165eb9.png

We get the following output. Note you can only use the critical value in Excel for a left-tail test.

clipboard_e8152e779885b13bf46b4c2c19e24756d.png

Excel for some reason only does the smaller tail area for the F-test, so you will need to double the p-value for a two-tailed test, p-value = 0.355275877*2 = 0.7106.

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  1. Hypothesis Testing Mean (Pop Standard Deviation Known) in Calculator

    hypothesis testing calculator standard deviation

  2. Standard Deviation With Examples: Using Scientific Calculator

    hypothesis testing calculator standard deviation

  3. Hypothesis Testing for Variance and Standard Deviation using a P-Value

    hypothesis testing calculator standard deviation

  4. Hypothesis testing tutorial using p value method

    hypothesis testing calculator standard deviation

  5. Chapter 7 Hypothesis Testing with One Sample Larson Farber

    hypothesis testing calculator standard deviation

  6. PPT

    hypothesis testing calculator standard deviation

VIDEO

  1. Two-Sample Hypothesis Testing

  2. Hypothesis Testing for the Standard Deviation with One Sample Using Statcrunch

  3. Practical Research 2 Module 5 Activity 4 Am I Accepted or Rejected Answer Key

  4. How to Find of Standard Deviation

  5. Hypothesis Tests Standard Deviation

  6. Hypothsis Testing in Statistics Part 2 Steps to Solving a Problem

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  1. Hypothesis Testing Calculator with Steps

    Hypothesis Testing Calculator. The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is ...

  2. Hypothesis Test Calculator

    Calculation Example: There are six steps you would follow in hypothesis testing: Formulate the null and alternative hypotheses in three different ways: H 0: θ = θ 0 v e r s u s H 1: θ ≠ θ 0. H 0: θ ≤ θ 0 v e r s u s H 1: θ > θ 0. H 0: θ ≥ θ 0 v e r s u s H 1: θ < θ 0.

  3. 27: Hypothesis Test for a Population Mean Given Statistics Calculator

    hypothesis test for a population mean given statistics calculator. Select if the population standard deviation, σ σ, is known or unknown. Then fill in the standard deviation, the sample mean, x¯ x ¯ , the sample size, n n, the hypothesized population mean μ0 μ 0, and indicate if the test is left tailed, <, right tailed, >, or two tailed ...

  4. t-test Calculator

    This t-test calculator allows you to use either the p-value approach or the critical regions approach to hypothesis testing! Enter your T-score and the number of degrees of freedom . If you don't know them, provide some data about your sample(s): sample size, mean, and standard deviation, and our t-test calculator will compute the T-score and ...

  5. 8.4: Hypothesis Test on a Single Standard Deviation

    Example 8.4.1 Exercise 8.4.2 References; Review; Formula Review; A test of a single standard deviation assumes that the underlying distribution is normal.The null and alternative hypotheses are stated in terms of the population standard deviation (or population variance).

  6. Hypothesis Testing Calculator

    Sample Mean: Sample Size: Population Mean (Null Hypothesis): Population Standard Deviation: Significance Level (Alpha): Perform Test Understanding Hypothesis Testing: A Guide to the Hypothesis Testing Calculator Hypothesis testing is a crucial statistical method used to make informed decisions about data and draw conclusions. Whether you're a student, researcher, or professional, a ...

  7. Z-test Calculator

    We use a t-test for testing the population mean of a normally distributed dataset which had an unknown population standard deviation.We get this by replacing the population standard deviation in the Z-test statistic formula by the sample standard deviation, which means that this new test statistic follows (provided that H₀ holds) the t-Student distribution with n-1 degrees of freedom instead ...

  8. Hypothesis Testing Standard Deviation (stats)

    Testing a Population. Standard Deviation (statistics) Enter your statistics, claim, tail test, and significance level in the table below. Sample Size, n. Sample Standard Deviation, s. Claim. Choose a Tailed Test. Choose a Level of Significance. Calculate.

  9. 28: Hypothesis Test for a Population Mean With Data Calculator

    Hypothesis Test for a Population Mean With Data Calculator. Type in the values from the data set separated by commas, for example, 2,4,5,8,11,2. Then type in the population standard deviation σ if it is known or leave it blank if it is not known. Then choose a left, right or two tailed test, and the hypothesized mean.

  10. Hypothesis Testing Standard Deviation (data)

    Testing a Population Standard Deviation (data) Input your values with a space or comma between in the table below. Enter data here. Claim. Choose a Tailed Test. Choose a Level of Significance. Calculate. Clear All. CRITICAL VALUES. Results shown here ... Results shown here. SAMPLE VARIANCE. Results shown here. Hypothesis Testing Std Dev Data ...

  11. Section 10.4: Hypothesis Tests for a Population Standard Deviation

    Performing a Hypothesis Test Regarding σ. Step 1: State the null and alternative hypotheses. Step 2: Decide on a level of significance, α. Step 3: Compute the test statistic, . Step 4: Determine the P -value. Step 5: Reject the null hypothesis if the P -value is less than the level of significance, α.

  12. Online Statistics Calculator: Hypothesis testing, t-test, chi-square

    Online Statistics Calculator: Hypothesis testing, t-test, chi-square, regression, correlation, analysis of variance, cluster analysis ... Mode Calculator Dispersion parameter Calculator Standard Deviation and Variance Calculator Range Calculator Frequency table Calculator Contingency table Calculator Hypothesis Testing Calculator p-Value ...

  13. Standardized Test Statistic Calculator

    A standardized test is scored in a standard manner. A statistical hypothesis test is a method of statistical inference. Subtract Sample Mean by Population Mean, divide Sample Standard Deviation by Sample Size and then divide both the answer in the below Standardized Test Statistic calculator to calculate Hypothesis Test for z-scores.

  14. Hypothesis Testing

    You can use the TI 83 calculator for hypothesis testing, but the calculator won't figure out the null and alternate ... Example problem: A sample of 200 people has a mean age of 21 with a population standard deviation (σ) of 5. Test the hypothesis that the population mean is 18.9 at α = 0.05. Step 1: State the null hypothesis. In this ...

  15. Z Test: Uses, Formula & Examples

    Population standard deviation is known. As I mention in the Z test vs T test section, use a Z test when you know the population standard deviation. However, when n > 30, the difference between the analyses becomes trivial. Related post: Standard Deviations. Z Test Formula. These Z test formulas allow you to calculate the test statistic.

  16. 8.3: Hypothesis Test Examples for Means with Unknown Standard Deviation

    Answer. Set up the hypothesis test: A 5% level of significance means that α = 0.05. This is a test of a single population mean. H0: μ = 65 Ha: μ > 65. Since the instructor thinks the average score is higher, use a " > ". The " > " means the test is right-tailed. Determine the distribution needed:

  17. One Sample T Test Calculator

    Unknown standard deviation. The one-sample t-test determines if the mean of a single sample is significantly different from a known population mean. The one sample t-test calculator calculates the one sample t-test p-value and the effect size. When you enter the raw data, the one sample t-test calculator provides also the Shapiro-Wilk normality ...

  18. Chi-Square test for One Pop. Variance

    The formula for a Chi-Square statistic for testing for one population variance is. \chi^2 = \frac { (n-1)s^2} {\sigma^2} χ2 = σ2(n−1)s2. The null hypothesis is rejected when the Chi-Square statistic lies on the rejection region, which is determined by the significance level ( \alpha α) and the type of tail (two-tailed, left-tailed or right ...

  19. T-test for two Means

    Instructions : Use this T-Test Calculator for two Independent Means calculator to conduct a t-test for two population means ( \mu_1 μ1 and \mu_2 μ2 ), with unknown population standard deviations. This test apply when you have two-independent samples, and the population standard deviations \sigma_1 σ1 and \sigma_2 σ2 and not known.

  20. 10.2: Two Population Means with Unknown Standard Deviations

    For the hypothesis test, we calculate the estimated standard deviation, or standard error, of the difference in sample means, \(\bar{X}_{1} - \bar{X}_{2}\). ... Their average is four math classes with a standard deviation of 1.5 math classes. College B samples nine graduates. Their average is 3.5 math classes with a standard deviation of one ...

  21. One Sample Variance Test Calculator

    Chi-square test for the variance. Target: To check if the assumed variance (σ 2 0) is statistically correct, based on a sample variance S 2. Identically check if the assumed standard deviation (σ 0) is statistically correct, based on a sample standard deviation S. Target: the chi-square test for the variance checks if the population variance (σ 2) is different from the expected value (σ 0 ...

  22. 9.4: Two Variance or Standard Deviation F-Test

    Based on a sample of 28 university students, the sample standard deviation 10, and for a sample of 25 community college students, the sample standard deviation 12. Test the claim using the traditional method of hypothesis testing with a level of significance \(\alpha\) = 0.05. Assume that IQ scores are normally distributed.