Stats homework please help

Question

A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You find that a random sample of 37 cardholders has a mean credit card debt of $5,122 and a standard deviation of $625. At 𝛼 = 0.01 can you support the claim.

(a) Construct the null and alternative hypothesis.

(b) Identify the degrees of freedom.

(c) What is the decision?

(d) Interpret the decision.

Answer 1

HO: Mean = 5000

HA: Mean > 5000

37-1 = 36 degrees of freedom

t-statistic = (5122-5000)/(625/square root(37)) = 1.187

P(t > 1.187) with 36 degrees of freedom = 0.1215, which is greater than 0.01.

Do not reject HO

There is not sufficient evidence that the mean credit card debt is greater than $5000