Question

A bank claims that the mean loan for individuals is greater than $7 000. We want to test this claim. We find that a random sample of 38 individuals with a loan has a mean loan of $7 183 and a standard deviation of $626. At α = 0.05, can we support the claim? Assume the population is normally distributed.

a) State the claim verbally and mathematically for the given problem.

b) What is the null hypothesis for the given problem?

c) What is the rejection region for the given problem?

d) What is the test statistic value for the given problem?

e) Interpret the results.

Answer 1

Solution :

a ) Given that

= 7000

=7183

S =626

n = 38

b ) This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 7000

Ha : > 7000

c ) The significance level is α=0.05, and the critical value for a right-tailed test is tc​=1.687

d ) Test statistic = t

= ( - ) / S / n

= (7183-7000) / 626 / 38

= 1.901

Test statistic = t = 1.901

P-value =0.0326

e ) = 0.05  

P-value <

0.0326 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that