Answer to Question #324569 in Statistics and Probability for mark

Question

A researcher used a developed problem-solving test to randomly selected 50 Grade-11 students. In this sample, X ̅=80 and s=10. The mean and standard deviation of the population used in the standardization of the test were 75 and 15, respectively. Use the 95% confidence level. What is the computed test statistic?

Answer 1

The test statistic is

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

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.