Explanation Calculation: The two sample t statistic is, t = ( x ¯ 1 − x ¯ 2 ) − ( μ 1 − μ 2 ) s 1 2 n 1 + s 2 2 n 2 In the formula, μ 1 is mean of first population, μ 2 is mean of second population, x ¯ 1 is the sample mean from population 1, x ¯ 2 is the sample mean from population 2, s 1 2 sample variance of population 1, s 2 2 is sample variance of population 2, n 1 is the sample size from population 1 and n 2 is the sample size from population 2. Let μ 1 denotes the violent crime rate in New England, μ 2 denotes the violent crime rate in the rocky mountain region. From the given information the value of α is 0.01, and the data indicate that the violent crime rate in the rocky mountain region is higher than that in New England. The null and alternative hypothesis is, Null hypothesis: H 0 : μ 1 = μ 2 Alternative hypothesis: H 1 : μ 1 < μ 2 The sample value is, x ¯ 1 − x ¯ 2 = 3.51 − 3.87 = − 0.36 The value of x ¯ 1 − x ¯ 2 is –0.36. T-statistic : Substitute x ¯ 1 as 3.51, x ¯ 2 as 3.87, μ 1 − μ 2 as 0, s 1 as 0

Understandable Statistics: Concepts And Methods

12th Edition

ISBN: 9781337517508

Author: Charles Henry Brase, Corrinne Pellillo Brase

Publisher: Cengage Learning

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Chapter 8.5, Problem 37P

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Check whether the null hypothesis is rejecting or fail to reject by using the critical region method.

Compare the conclusion of critical value method with the P-value method.

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Chapter 8.5, Problem 36P

Chapter 8.5, Problem 38P

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You may need to use the appropriate technology to answer this question. We want to test whether or not the addition of 3 variables to a model will be statistically significant. You are given the following information based on a sample of 25 observations. ý = 62.480 – 1.838x + 25.660X2 SSE = 745; SSR = 596 The model was also estimated including the 3 variables. The results are: ŷ= Ỹ = 59.220 – 1.766xq + 25.635X, + 16.239Xg + 15.296x4 – 18.729X, SSE = 540; SSR = 801 (a) State the null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B3 = P4=B5 O Ho: P₁ = P₂ = B3 = P4=B5 = 0 H₂: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = B₂ = B3 =B4 =B5 = 0 Ho: B3 = P4 = B ₁ = 0 H₂: One or more of the parameters is not equal to zero. (b) Test the null hypothesis at the 5% level of significance. Find the value of the test statistic. (Round your answer to two decimal places.) 2.53 X Find the…

Can you do b please

You may need to use the appropriate technology to answer this question. We want to test whether or not the addition of 3 variables to a model will be statistically significant. You are given the following information based on a sample of 25 observations. y = 62.480 1.838x₁ + 25.660x₂ - SSE = 745; SSR = 596 The model was also estimated including the 3 variables. The results are: ŷ ý = 59.220 – 1.766x + 25.635X, + 16.239Xg + 15.296X4 – 18.729x5 SSE = 540; SSR = 801 (a) State the null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B3 = P4=B5 O Ho: B₁ = B₂= B3 =B4=B5= H₂: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = B₂= B3 = P4 = B 5 = 0 ⒸH₁: B3 =B4 = ß5 = 0 H₂: One or more of the parameters is not equal to zero. ✓ (b) Test the null hypothesis at the 5% level of significance. Find the value of the test statistic. (Round your answer to two decimal places.) 5.64 X Find the…

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Check whether the null hypothesis is rejecting or fail to reject by using the critical region method. Compare the conclusion of critical value method with the P -value method.

Solution Summary: The author compares the conclusion of critical value method with the P -value method. The null hypothesis is not rejected.

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Check whether the null hypothesis is rejecting or fail to reject by using the critical region method.

Compare the conclusion of critical value method with the P-value method.

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Chapter 8 Solutions

Check whether the null hypothesis is rejecting or fail to reject by using the critical region method. Compare the conclusion of critical value method with the P -value method.

Solution Summary: The author compares the conclusion of critical value method with the P -value method. The null hypothesis is not rejected.

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Check whether the null hypothesis is rejecting or fail to reject by using the critical region method. Compare the conclusion of critical value method with the P-value method.

Want to see the full answer?

Chapter 8 Solutions

Check whether the null hypothesis is rejecting or fail to reject by using the critical region method.

Compare the conclusion of critical value method with the P-value method.