The following output from MINITAB presents the results of a hypothesis test. Test of mu=49 vs. not=49, The assumed standard deviation 10.4, N 58, Mean 46.32, SE 1.412088, 95%CI (43.5523077, 49.0878923, Z -1.962526, P 0,049701, Do you reject H0 at the
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is rejected.Therefore, there is enough evidence to claim that the population mean is different than 49, at the significance level.
The corresponding 95% confidence interval is
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