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The critical value for is The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 95% confidence interval for the population mean is which indicates that we are 95% confident that the true population mean is contained by the interval
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 at the significance level.