Assume that the population is normally distributed and that the sample has been randomly selected and test the given claim. 4) Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Use the traditional method of testing hypotheses.. 62.13 65.09 64.18 66.72 63.09 61.15 67.50 64.65 63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72 (a) Set up the null hypothesis and alternative hypothesis and indicate the claim. (b) Calculate the test statistic. Round to three decimal places. (c) Find the critical value(s). Draw a sketch of the distribution curve and indicate the significance level and the critical value(s) on the graph.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Problem Statement:**
Assume that the population is normally distributed and that the sample has been randomly selected to test the given claim.

4) Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Use the traditional method of testing hypotheses.

**Data:**
62.13, 65.09, 64.18, 66.72, 63.09, 61.15, 67.50, 64.65  
63.80, 64.21, 60.17, 68.28, 66.49, 62.10, 65.73, 64.72  

**Tasks:**

(a) **Set up the null hypothesis and alternative hypothesis and indicate the claim.**

(b) **Calculate the test statistic.** Round to three decimal places.

(c) **Find the critical value(s).** Draw a sketch of the distribution curve and indicate the significance level and the critical value(s) on the graph.

(d) **Make a decision about the null hypothesis.** Be sure to explain how you make the decision.

(e) **Draw a conclusion about the original claim.** 

**Instructions for the Diagram:**

(c) When drawing a sketch of the distribution curve:
- Label the x-axis with the distribution of the test statistic.
- Mark the critical value(s) according to the significance level (0.05).
- Shade the area representing the rejection region(s).
- Indicate the critical value(s) on the curve.
Transcribed Image Text:**Problem Statement:** Assume that the population is normally distributed and that the sample has been randomly selected to test the given claim. 4) Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Use the traditional method of testing hypotheses. **Data:** 62.13, 65.09, 64.18, 66.72, 63.09, 61.15, 67.50, 64.65 63.80, 64.21, 60.17, 68.28, 66.49, 62.10, 65.73, 64.72 **Tasks:** (a) **Set up the null hypothesis and alternative hypothesis and indicate the claim.** (b) **Calculate the test statistic.** Round to three decimal places. (c) **Find the critical value(s).** Draw a sketch of the distribution curve and indicate the significance level and the critical value(s) on the graph. (d) **Make a decision about the null hypothesis.** Be sure to explain how you make the decision. (e) **Draw a conclusion about the original claim.** **Instructions for the Diagram:** (c) When drawing a sketch of the distribution curve: - Label the x-axis with the distribution of the test statistic. - Mark the critical value(s) according to the significance level (0.05). - Shade the area representing the rejection region(s). - Indicate the critical value(s) on the curve.
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