Researchers are concerned about the impact of students working while they are enrolled in classes, and they’d like to know

if students work too much and therefore are spending less time on

their classes than they should be. First, the researchers need to find

out, on average, how many hours a week students are working They know from previous studies that the standard deviation of this

variable is about 5 hours.

(i) A survey of 200 students provides a sample mean of 7.10

hours worked. 95% confidence interval based on this sample is

6.41 to 7.79.

Do you agreed with the researcher that the 95% confident interval of

the unknown population mean of the students worked hours lies

between 6.41 and 7.79?

Indicate whether the researchers are right or wrong, giving reasons

for your answer.

(ii) Based on your understanding of confident interval estimation;

explain the reason why the researcher did not use 100% confidence

level, but instead he used 95% confidence level.

(iii) The researchers are not satisfied with their confidence interval

and want to do another study to find a shorter confidence interval.

What should they change to ensure they find a shorter confidence interval?