Question

A credit card company claims that the mean credit card debt for individuals is greater than $5,300. You want to test this claim. You find that a random sample of 38 cardholders has a mean credit card balance of $5,533 and a standard deviation of $ 550. At α=0.05, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identify H0 and Ha. What is(are) the critical value(s), t0? Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) c) Find the standardized test statistic t.

Answer 1

Here claim is that the mean credit card debt for individuals is greater than $5,300

a. Hypothesis is vs

b. The z-critical value for a right-tailed test, for a significance level of α=0.05 is

zc​=1.64

Graphically

c. Here n=38>30, so we can use z distribution

As test statistics falls in the rejection region we reject the null hypothesis

Hence we have sufficient evidence to support the claim that the mean credit card debt for individuals is greater than $5,300