Question

Consider the following hypothesis test: Ho: ?> 45 Ha: ? < 45 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use ? four decimals for p-value questions. a. With - 44 and s - 5.2, the p-value is -Select your answer- Can it be concluded that the population mean is less than 45? .01 and Select b. With 43 and s 4.6, the p-value isSelect your answer Can it be concluded that the population mean is less than 45? Select c. With 46 and s 5.0, the p-value is - Select your answer Can it be concluded that the population mean is less than 45? Select

Answer 1

Answer Date: 19/04/2018 To test the hypothesis is that the population mean is less than 4 5 at 1 % significance level The null and alternative hypothesis is, Ha:μ<45 a) The p-value for this test is, By using Excel, findp-value with the help of following steps is: 1) Import the data 2) Select the MegaStat from Add-Ins Menu 3) Select Mean vs. Hypothesized Value from Hypothesis Tests. 4)Enter Summary Input and Hypothesized mean. 5) Select t-test, Alternative and Confidence Level. 6) Click Ok.

Hypothesis Test: Mean vs. Hypothesized Value 45.00 hypothesized value 44.00 mean Sample 5.20 std. dev. 0.87 std. error 36 n 35 df 1282 p-value (one-tailed, lower) From the Excel output, the p-value for this test is 0.1282 Decision The conclusion is that the p-value in this context is greater than 0.01 which is 0.1282, so the null hypothesis is not rejected at 1% level of significance. There is insufficient evidence to indicate that the population mean is less than 45. The result is not statistically significant b)

The p-value for this test is By using Excel, findp-value with the help of following steps is: 1)Import the data 2) Select the MegaStat from Add-Ins Menu. 3) Select Mean vs. Hypothesized Value from Hypothesis Tests 4)Enter Summary Input and Hypothesized mean. 5) Select t-test, Alternative and Confidence Level. 6) Cick Ok. Hypothesis Test: Mean vs. Hypothesized Value 45.00 hypothesized value 43.00 mean Sample 4.60 std. dev. 0.77 std. error 36 n 35 df -2.61t 0066 p-value (one-tailed, lower) From the Excel output, the p-value for this test is 0.0066

Decision The conclusion is that the p-value in this context is less than 0.01 which is 0.0066, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the population mean is less than 45. The result is statistically significant. c) The p-value for this test is, By using Excel, find p-value with the help of following steps is 1)Import the data 2)Select the MegaStat from Add-Ins Menu 3)Select Mean vs. Hypothesized Value from Hypothesis Tests. 4)Enter Summary Input and Hypothesized mean. 5) Select t-test, Alternative and Confidence Level. 6) Click Ok.

Hypothesis Test: Mean vs. Hypothesized Value 45.00 hypothesized value 46.00 mean Sample 5.00 std. dev. 0.83 std. error 36 n 35 df 1.20 8809 t p-value (one-tailed, lower) From the Excel output, thep-value for this test is 0.8809 Decision The conclusion is that the p-value in this context is higher than 0.01 which is 0.8809, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that the population mean is less than 45. The result is not statistically significant.