Question

Using the CI for the mean formula answer the following question:

Suppose in a class of 60 students the class scores for the final exam in general are normally distributed with a mean of 150 and a standard deviation of 20.85. Suppose the instructor suggest the students watch a video just before they take the final exam to see if the scores increase. After watching the video, the mean of the 60 students increased to 155.67. Construct a 95% CI for μ and interpret the results. (Show your work)

Answer 1

Given that

sample size n = 60

mean xbar = 155.67

and standard deviation sigma = 20.85

z critical value for 95% confidence level is 1.96 (using z table)

Confidence interval =

We are 95% confident that the true mean score for the class is between (150.394, 160.946).

We can see that the population mean value of 150 is not included in the confidence interval, this means that the watching a video just before taking the final exam significantly increases scores.