A sample of 160 people has a mean age of 27 with a population standard deviation of 5. Test the hypothesis that the population mean is 26.7 at =0.05
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:
6. Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for two-tailed is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean
is different than 26.7, at the significance level.
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