## 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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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

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3. 3c. A. B. Women have head circumferences that are normally distributed with a mean of 23.55 inches and a standard deviation of 0.93 inches. If the HATS BY CHARLIE company produced hats so that they fit head circumferences between 22.2 inches and 24.2 inches, then what is the probability that a woman can fit into these hats? A. If the HATS BY CHARLIE company produced hats so that they fit head circumferences between 22.2 inches and 24.2 inches, then what is the probability that a randomly selected group of 40 woman can fit into these hats? B. Write a sentence or two that explains your answer to 3B and why you think that answer is correct in connection to your answer in 3A.
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.
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 a = 0.05. Z-Test Inpt: Data Stats u + 60 Ho:60 0:4.75 x:58.25 n:45 Z-Test z= - 2.47144355 p = 0.01345688 x = 58.25 In = 45 Calculate Draw Orl Orl + Choose the correct answer below. O A. Since the P-value is less than a, fail to reject the null hypothesis. B. Since the P-value is less than a, reject the null hypothesis. O C. Since the P-value is greater than a, fail to reject the null hypothesis. O D. Since the P-value is greater than a, 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
Results of a research claim to predict wind speed at a place with a variance of 4 km/hr or less. A random sample of 24 measurements provides a sample variance of s2 = 4.9. Assuming that the population distribution of wind speed is approximately normal, check the validity of the claim at 5% level of significance using chi-square test.
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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