Question

Problem 1 – Estimation of study hours

A random sample of 20 students drawn from a student population in a very large public university. It is found that the 20 selected students studied on average 16.4 hours per week outside class contact time. Assume that study hours outside class contact time is normally distributed. Also assume that the population standard deviation on study hours outside class contact time is 5.5 hours per week. Construct a 98 percent confidence interval for the population average hours that students study outside class contact time per week.

a) Specify the appropriate formula you would use to solve the problem. Provide a brief reason why you chose the formula. 1 mark

b) Obtain the 98% lower and upper confidence limits of the true population average hours that students study outside class contact time per week. Display working. 3 marks

c) Provide an interpretation of the lower and upper confidence limits you obtained in part b) in the context of the problem.

2 marks

d) Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when a lower level of significance is used? 1 mark

e) Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when the value of the sample mean increases? 1 mark

Answer 1

If we calculate the two tailed t test for degree of freedom 19 and percent of the student study outside the class at 98% confidence:

It is +/- 2.5395

So range fo the student studying in the lower side is :

-2.5395 = (x-16.4)/(5.5/sqrt(20))

-3.1231 =(X -16.4)

X = 16.4-3.1231

X = 13.2768

And upper side:

2.5395 = (x-16.4)/(5.5/sqrt(20))

3.1231 =(X -16.4)

X = 16.4+3.1231

X = 19.5231

Answer A:

to find the t value at 98% confidence interval for degree of freddom 19 as sample size is less than 30 so we will use the two tail t test

Answer B:

Lower limit is 13.2768 hour and upper limit is 19.5231 with 98 % confidence interval

Answer C:

The population mean of studying hour outside the class lies within 13.2768 hours to 19.5231 hours with 98% confidence interval