Question

A research is interested in whether the mean score on a particular aptitude test for students who attend rural elementary schools is higher than the score of elementary school students in general (ux=50), ox=10). She tests a random sample of 28 rural elementary school students and finds the sample mean to be 56.

Using alpha=.05, conduct the 8 steps hypothesis testing to determine whether the rural elementary school students have a significantly higher aptitude score than elementary students in general.

Answer 1

The provided sample mean is and the known population standard deviation is σ=10, and the sample size is n=28.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is Zc​=1.64.

The rejection region for this right-tailed test is R={z:z>1.64}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z=3.175>zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0007, and since p=0.0007<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 50, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval is 52.296<μ<59.704.

Graphically

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