Answer to Question #308328 in Statistics and Probability for AAA

Question

A researcher used a developed problem solving test to randomly select 50 grade 6 pupils. In this sample,  x̄= 80. The mean μ and the standard deviation of the population used in the standardization of the test were 75 and 15, respectively. Test the hypothesis that the sample mean differ significantly from the population mean. Use level of significance 0.05. The z value is 1.96.

Answer 1

The test statistic is

$Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{50}\frac{80-75}{15}=2.35702$

Since the absolute value of the statistic is greater than 1.96, the null hypothesis (that the means are equal) is rejected. The means differ significantly.