Test of hypothesis involving the population mean 𝝁 when the variance is known

[bunnypatotie]

1. The Head of the Mathematics Department announced that the mean score of Grade 11 students in the second periodical test in Statistics was 89, and the standard deviation was 12. One student believed that the mean score was less than this, randomly selected 34 students, computed their mean score, and obtained a mean score of 85. At 0.01 level of significance, test the student’s belief.

- I'm confused on what test statistic to use. I think z-statistic and CLT are both possible for this problem.

 

[Valkarie]

Answer:We can use the one-sample z-test to determine if the student's belief is valid. The null hypothesis is that the mean score of Grade 11 students in the second periodical test in Statistics is equal to 89. H0: μ = 89The alternative hypothesis is that the mean score is less than 89.Ha: μ < 89The test statistic is calculated as follows:z = (85 - 89)/(12/√34) = -2.36The critical value at a 0.01 level of significance is -2.33. Since the test statistic is less than the critical value, we reject the null hypothesis and conclude that the student's belief that the mean score was less than 89 is supported at the 0.01 level of significance.