Question

6. Testing a population mean, Methods (Exercise 9.23 eBook Consider the following hypothesis test: Ho: ? 12 Ha: ? > 12 A sample of 25 provided a sample mean T -14 and a sample standard deviation s 4.32. a. Compute the value of the test statistic (to 2 decimals). b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value. The p-value is Select Answer the next three questions using the critical value approach. C. Using ?-.05, what is the critical value for the test statistic? d. State the rejection rule: Reject Ho if t is Select e. Using ?-.05, can you conclude that the population mean is greater than 12? the critical value. Select

Answer 1

Given that population mean μ-12, Stan dard deviation, S-4.32, Sanpl mean ? 14 Sample size n -25,(Small Sample) The Null Hypothesis, Ho , щ£12 The alternative Hypothesis, H1: μ>120 ught tail test) Level of significance: α-005 (95% Confidence for right tail test) with n-1-24 degrees of freedom is 2.06 2) The critical value is 2.06 (From standard normal table, z“ , at 0.01 LOS) 4322.31 b) p- valu F2.31)-F(2.06) 0.9893-0.98030.009 c)The critical valueis +2.06 d)Criterion at 0.05 LOS with 24 df for right tail testis taccept H0, otherwise Re ject H, e) Conclusion t 2.31 > 2.06-Z, Reject Ho Hence the populationmean S12.