**14.5 Testing for Significance****EXERCISES****Methods****23.** The data from exercise 1 follow. | \( x_i \) | 1 | 2 | 3 | 4 | 5 ||-----------|---|---|---|---|---|| \( y_i \) | 3 | 7 | 5 | 11 | 14 |a. Compute the mean square error using equation (14.15).b. Compute the standard error of the estimate using equation (14.16).c. Compute the estimated standard deviation of \( b_1 \) using equation (14.18).d. Use the \( t \) test to test the following hypotheses (\( \alpha = .05 \)): \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \]e. Use the \( F \) test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.**24.** The data from exercise 2 follow.| \( x_i \) | 3 | 12 | 6 | 20 | 14 ||-----------|---|----|---|----|----|| \( y_i \) | 55| 40 | 65| 10 | 15 |a. Compute the mean square error using equation (14.15).b. Compute the standard error of the estimate using equation (14.16).c. Compute the estimated standard deviation of \( b_1 \) using equation (14.18).d. Use the \( t \) test to test the following hypotheses (\( \alpha = .05 \)): \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \]e. Use the \( F \) test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.**25.** The data from exercise 3 follow.| \( x_i \) | 2 | 6 | 9 | 13 | 20 ||-----------|---|---|---|----|

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Description: **14.5 Testing for Significance****EXERCISES****Methods****23.** The data from exercise 1 follow. | \( x_i \) | 1 | 2 | 3 | 4 | 5 ||-----------|---|---|---|---|---|| \( y_i \) | 3 | 7 | 5 | 11 | 14 |a. Compute the mean square error using equation (

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Methods 23. The data from exercise 1 follow. X3B 1 2 3 4 5 Yi 3 7 5 11 14 a. Compute the mean square error using equation (14.15). b. Compute the standard error of the estimate using equation (14.16). c. Compute the estimated standard deviation of b, using equation (14.18). d. Use the t test to test the following hypotheses (a = .05): Ho: B, = 0 HiB, #0 e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

Methods 23. The data from exercise 1 follow. X3B 1 2 3 4 5 Yi 3 7 5 11 14 a. Compute the mean square error using equation (14.15). b. Compute the standard error of the estimate using equation (14.16). c. Compute the estimated standard deviation of b, using equation (14.18). d. Use the t test to test the following hypotheses (a = .05): Ho: B, = 0 HiB, #0 e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

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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Test A was developed as a possible replacement for Test B. It was claimed that the mean time to complete Test A was more than the mean time to finish Test B. (a) At α = 5%, use the Classical approach to conclude it. (b) Using the P-value approach to conclude it. Please see a summary of data for completion times below: Test A : n=7, X bar=158 minutes, S2=165 minutes Test B : n=11 X bar=152 minutes, S2=33 minutes Estimate of standard error=16 **Notes-P-value: Using t-distribution, the p-value is equal to 0.1307 for a one-tailed test. P-value 0.1307> significance level a=0.10, therefore, we fail to reject. Additionally, there is not enough evidence to support the claim that mean time to complete the new test A is more than the meantime to complete test B.
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7. Sketch two normal curves on the axis below with approximately equal standard deviations, one with a mean of 7 and the other with a mean of 12. 7 10 II 12 13 14 15 00 2.
You may need to use the appropriate technology to answer this question. Consider the data. xi 1 2 3 4 5 yi 4 8 6 12 15 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi − x)2 . (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (? = 0.05): H0: ?1 = 0 Ha: ?1 ≠ 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 = State your conclusion. Reject H0. We cannot conclude that the relationship between x and y is significant.Do not reject H0. We conclude that the…
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A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =
Two accounting professors decided to test if the variance of their grades is different or no. To accomplish this, they each graded the same 10 exams with the following results: Standard Grade þeviation 22.4 12.0 Мean Professor 1 Professor 2 79.3 82.1 F What is the P-value of the test? Select one: Oa. between 0.01 and 0.025 Ob. between 0.025 and 0.05 c. between 0.05 and 0.10 Od. bigger than 0.10
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The yield per tract in a certain region of farmland is known to have a populationstandard deviation of 13 bushels. Using the old seed variety, the population mean yield μwas 39 bushels. A farmer tests a new seed variety on a random sample of 36 tracts, andfinds a sample mean yield of 45.2 bushels. Is the population mean yield using the newseed variety different from 39? Use α= 0.10.a. State the null hypothesis . __________________State the alternative hypothesis.____________________b. Find the test statistic. _____ c. Find the P-value for the test. _____________
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