Question

Five years ago the average university student owed $19,000 in student-loan debt at the time of graduation. With all the cuts in funding, it is suspected that this amount has gone up. A survey of 45 recent university graduates revealed an average student-loan debt of $20,000. Assume that the population standard deviation is $2,500.

a) Define the parameter of interest (in words), and then formulate the null hypothesis and the alternative hypotheses.

b) Find the p-value and make a conclusion in the context of the question. Use a level of significance of 5% (i.e. α = 0.05).

Answer 1

Solution :

= 19000

=20000

=2500

n = 45

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    =19000

Ha :     19000

Test statistic = z

= ( - ) / / n

= (19000 -20000 ) /2500 / 45

= -2.68

Test statistic = z = -2.68

P-value = 2 * 0.0037 =0.0074

= 0.05  

P-value <

0.0074 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that