Question

The Office of the Registrar at Brock University is studying student midterm grades in a particular Canadian history course. They randomly select 10 students from the course and document their scores from the midterm, which are given below (in percentages):

53, 67, 81, 72, 59, 48, 61, 68, 64, 57

Assuming the population is approximately normaland using a 0.05significance level, test theclaim that the mean test score for the entire class is greater than 60.

State the null and alternative hypotheses.
Calculate the test statistic (roundit to 3 decimal places).
Find the critical value (round it to 3 decimal places).
Make a decision and write a conclusion based on your answers from parts b) and c).

Answer 1

The null hypothesis (H₀): The mean test score for the entire class is equal to or less than 60.

The alternative hypothesis (H₁): The mean test score for the entire class is greater than 60.

The calculated test statistic is 1.005.

The critical value at a significance level of 0.05 is 1.833.

Based on the test statistic being less than the critical value, we fail to reject the null hypothesis. There is not enough evidence to support the claim that the mean test score for the entire class is greater than 60.

Explanation:

The null hypothesis assumes that the mean test score for the entire class is equal to or less than 60, while the alternative hypothesis suggests that it is greater than 60. With a sample size of 10 and a known population standard deviation, a one-sample z-test was conducted to assess these hypotheses.

The calculated test statistic, rounded to 1.005, was lower than the critical value at a 0.05 significance level, which was 1.833. Consequently, we fail to reject the null hypothesis. This means there isn't sufficient evidence from the sample to support the claim that the mean test score for the entire class exceeds 60. Therefore, based on this analysis, there isn't enough statistical significance to conclude that the mean test score for the entire class is greater than 60.

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