Question

A credit card company lowered its annual interest rate recently. Records showed that before the rate change, the average outstanding balance on a credit card was $580. The managers believed that if they lowered interest rates that this would increase the average outstanding balance. To test this claim, a random sample of 30 accounts was examined after the rate decrease. The average outstanding balance of this sample was $620 with a standard deviation of $105. At a 5% significance level, can it be concluded that the lower interest rate resulted in average account balance greater than $580?

a) Set up the null and alternative hypotheses in English and in mathematical symbols.

In words:

In math symbols: H_o: , H_a:

b) State the sample size, sample mean and sample standard deviation.

c) State the mean and standard error for the sampling distribution. Sketch the sampling distribution and label the mean, standard error, the observed value, and shade in the region for the P-value.

d) Find the test statistic, P-value, and state your conclusion in complete sentence(s).

Answer 1

solution:

a)

null hypothesis: if interest rates decreased , the outstanding balance on card remain same as before i,e $580

alternative : if interest rate decreased , the outstanding balance on card increase than $580

b) sample size = n = 30

sample mean = = $ 620

sample standard deviation = S = $105

C)

mean of sampling distribution =

standard error of sampling distribution =

d)

since population standard deviation is not known so we use t distribution

test statistics

significance level = = 0.05

degree of freedom = df = n-1 = 30-1 = 29

p value = 0.0227

since p value 0.0227 < 0.05, so rejecting the null hypothesis

conclusion :

there is sufficient evidence to conclude that the mean outstanding balance is increased when lowering the interest rates.