# The marks of DMT students results in June 2020 sessional examinations were normally disyributed with a mean pass mark of 9 and a standard deviation pa

The marks of DMT students results in June 2020 sessional examinations were normally disyributed with a mean pass mark of 9 and a standard deviation pass mark of 0.15. After moderation, a sample of 30 papers was selected to see if the mean pass mark had changed. The mean pass mark of the sample was 8.95. a) Find the $95\mathrm{%}$ confidence interval of students mean mark. b) Calculate for the critical regions of the $95\mathrm{%}$ confidence intervals. c) Using your results in "a" and "b" above, is there evidence of a change in the mean pass mark of the DMT students.
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Willie

Step 1 Let 'X' be the marks of students a) The formula for the confidence interval is The sample size and sample mean are given to be, $n=30$
$\stackrel{―}{x}=8.95$ The z-critical value at $\alpha =0.05$ is 1.96

b) The critical regions for $95\mathrm{%}$ confidence interval are Step 2 c) The hypotesis are:
The test statistics is given by:

The p-value lies between 0.0336 and 0.0344 p-value is greater than the alpha level of significance 0.025, ther null hypotesis is accepted. Conclusion: There is a lack of evidence in the mean pass marks of the students.