**Problem 8: Statistical Test on GPA Variance**A high school principal claims that the variance in the GPA of students in the graduating class is less than 0.39. You test this claim by sampling 31 seniors and find their GPA has a variance of 0.21.**Hypotheses:**- Null Hypothesis $ H_0: \sigma^2 = 0.39 $- Alternative Hypothesis $ H_a: \sigma^2 < 0.39 $ (Claim)The question asks if there is enough evidence to reject $ H_0 $ and support the principal’s claim at a 0.10 level of significance.**Options:**A. No, the test statistic $\chi^2 = 20.599$ is not in the rejection region with critical value 21.434B. No, the test statistic $\chi^2 = 16.154$ is not in the rejection region with critical value 40.256C. Yes, the test statistic $\chi^2 = 20.599$ is in the rejection region with critical value 16.154D. No, the test statistic $\chi^2 = 21.434$ is not in the rejection region with critical value 20.599E. Yes, the test statistic $\chi^2 = 16.154$ is in the rejection region with critical value 20.599The correct approach would be to compare the test statistic $\chi^2$ with the critical value to determine if the results fall into the rejection region, thereby justifying rejecting the null hypothesis in favor of the alternative hypothesis.

We have given that, Sample variance (s^2) = 0.21 Population variance (σ^2) = 0.39 Sample size (n) =…

Answered: A high school principal claims that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You work for a soft-drink company in the quality control division. You are interested in the variance of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the variance to be as low as possible. You gather a random sample of 16 containers. Estimate the population variance at a 80% level of confidence. 11.82 11.83 11.85 11.89 11.9 11.97 12 12 12 12.01 12.02 12.04 12.05 12.11 12.16 12.18 Variance of Data: 0.012 Note: Round all values to 3 decimals and use those rounded values in subsequent calculations. a) Find the lower and upper x critical values at 80% confidence: Lower: Upper: b) Report your confidence interval for o?: Lower Bound: Upper Bound:
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The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use ? = 0.10. State the null and alternative hypotheses. -H0: ?12 > ?22 Ha: ?12 ≤ ?22 -H0: ?12 ≠ ?22 Ha: ?12 = ?22 -H0: ?12 ≤ ?22 Ha: ?12 > ?22 -H0: ?12 = ?22 Ha: ?12 ≠ ?22 Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to four decimal places. Remember: When using WebAssign technology to find p-values, use the entire test statistic (not the rounded answer from the previous question.)) p-value = ?? State your conclusion. -Reject H0. We can conclude that there is a difference between the population variances. -Do not reject H0. We cannot conclude that…
0. A high school principal claims that the variance in the GPA of students in the graduating class is Tess than 0.39. You test this claim by sampling 31 seniors and find their GPA have a variance or 0.21. Ho:o? Ha:o2 < 0.39 (Claim) = 0.39 Is there enough evidence to reject Ho and support the principal's claim at a 0.10 level of significance? ohs A. No, the test statistic x? B. No, the test statistic x2 = 16.154 is not in the rejection region with critical value 40.256 C. Yes, the test statistic x? D. No, the test statistic x2 = 21.434 is not in the rejection region with critical value 20.599 E. Yes, the test statistic x? = 16.154 is in the rejection region with critical value 20.599 = 20.599 is not in the rejection region with critical value 21.434 %3D 20.599 is in the rejection region with critical value 16.154 %D
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