## Hypothesis Testing for Variances### Problem StatementTest the hypothesis that $ \sigma_1 > \sigma_2 $ at the $ \alpha = 0.01 $ level of significance for the given sample data.### Sample DataThe sample data for two populations is provided in the following table:| | Population 1 | Population 2 ||----------|--------------|--------------|| **n** | 61 | 31 || **s** | 34.4 | 27.6 |### Hypothesis TestingWe are testing the hypothesis $ H_0: \sigma_1 \le \sigma_2 $ against the alternative hypothesis $ H_1: \sigma_1 > \sigma_2 $. The test statistic for comparing two variances is the F-statistic.### Decision CriteriaCalculate the F-statistic and compare it with the critical value from the F-distribution table at the $ \alpha = 0.01 $ significance level.### Options for the Test Statistic and Critical Value- $ \circ $ Test statistic: $ F = 1.25 $. Critical value = 2.21. Do not reject $ H_0 $.- $ \circ $ Test statistic: $ F = 1.55 $. Critical value = 2.03. Reject $ H_0 $.- $ \circ $ Test statistic: $ F = 1.55 $. Critical value = 2.21. Do not reject $ H_0 $.- $ \circ $ Test statistic: $ F = 42.88 $. Critical value = 2.03. Reject $ H_0 $.Make sure to select the correct F-statistic and corresponding critical value, and then apply the decision rule to determine whether to reject or not reject the null hypothesis $ H_0 $.

Name: ## Hypothesis Testing for Variances### Problem StatementTest the hypo
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Description: ## Hypothesis Testing for Variances### Problem StatementTest the hypothesis that $ \sigma_1 > \sigma_2 $ at the $ \alpha = 0.01 $ level of significance for the given sample data.### Sample DataThe sample data for two populations is provided in t

The critical value from F distribution table at right tail test at n1-1 , n2-1 degree of freedom…

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Statistics

est the hypothesis that o1 > 02 at the a = 0.01 level of significance for the giv Population 1 Population 2 %3D 61 31 34.4 27.6 D Test statistic: F = 1.25. Critical value 2.21. Do not reject Hg. %3D %3D O Test statistic: F = 1.55. Critical value = 2.03. Reject Ho- %3D O Test statistic: F = 1.55. Critical value = 2.21. Do not reject Ho. Tart statistic:- F = 42. 88. Critical value = 2.03. Reject Ho-

est the hypothesis that o1 > 02 at the a = 0.01 level of significance for the giv Population 1 Population 2 %3D 61 31 34.4 27.6 D Test statistic: F = 1.25. Critical value 2.21. Do not reject Hg. %3D %3D O Test statistic: F = 1.55. Critical value = 2.03. Reject Ho- %3D O Test statistic: F = 1.55. Critical value = 2.21. Do not reject Ho. Tart statistic:- F = 42. 88. Critical value = 2.03. Reject Ho-

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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Use the calculator displays to the right to make a decision to reject or fail to reject the null hypothesis at a significance level of α=0.05. Z-Test Z-Test Inpt: Data Stats μ≠50 μ0:50 z=−1.40859042 σ:5.25 p=0.15895631 x:48.75 x=48.75 n:35 n=35 μ: ≠μ0 <μ0 >μ0 Calculate Draw Choose the correct answer below. A. Since the P-value is greater than α, reject the null hypothesis. B. Since the P-value is less than α, reject the null hypothesis. C. Since the P-value is less than α, fail to reject the null hypothesis. D. Since the P-value is greater than α, fail to reject the null hypothesis.
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Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand Price ($) Score 180 74 В 150 69 95 63 70 56 70 40 F 35 28 (a) The estimated regression equation for this data is ý = 25.870 + 0.291x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. O Ho: Bo * 0 H: Bo = 0 O Ho: B1 20 Hoi Bq < 0 O Ho: Bo = 0 Hg: Bo 0 O Ho: B1* 0 H: B, = 0 O Ho: B, = 0 H: B1 = 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Do not reject H. We conclude that the relationship between price ($) and overall score is significant. O Do not reject…
25 versus H1: µ 7 25. The population variance, o?, ', is Suppose you perform the hypothesis test Ho :u known. The sample size is n = 53. Assume the significance level is 0.01. Part 1: 1) Should you use z or t to find the critical value? Ot Part 2 of 4 Part 2: 2) Choose the correct critical region. Reject Ho if z > Za Reject Ho if z za Reject Ho if z Reject Ho if z Za O Reject Ho if z > zg Reject Ho if z Za Reject Ho if z < Za Reject Ho if z < Za or z za Reject Ho if z < Za O Reject Ho if z < - zg or z 2 z
Calculate a Pearson’s r using the following set of raw scores. participant X Y A 12 8 B 17 3 C 22 2 D 8 18 E 13 5 F 15 5 G 20 3 H 12 7 I 5 21 1) Calculate the Pearson's r 2) Calculate r^23) Determine the critical value(s) (for an alpha of .05, two-tailed) that should be used to testthis r for statistical significance.
decimal equivalent to 3/2pi
Suppose you perform the hypothesis test Ho: u = 80 versus H1:µ + 80. The population variance, o, is unknown. The sample size isn = 13. Assume the significance level is 0.09. Part 1: 1) Should you use z or t to find the critical value? t Part 2 of 4 Part 2: 2) Choose the correct critical region. Reject Ho if t > ta Reject Ho if t ta Reject Ho if t ta Reject Ho if t ta O Reject Ho if t 2 tę Reject Ho if t s - ta or t > ta O Reject Ho if t t Reject Ho if t < – ta O Reject Ho if t < - t; ort 2 tę
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