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The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations 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 not rejected.
Using the P-value approach:
The p-value 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 at the significance level.