A researcher used a developed problem solving test to randomly select 50 Grade 6 pupils. In
this sample, and . The mean and the standard deviation of the population used in
the standardization of the test were 75 and 15, respectively. Use the 95% confidence level
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 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 75, at the significance level.
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