Question

A credit card company claims that the mean credit card debt for individuals is greater than $ 5,000. You want to test this claim. You find that a random sample of 34 cardholders has a mean credit card balance of $ 5,228 and a standard deviation of $ 550. At alpha equals 0.10​, can you support the​ claim? Complete parts​ (b) through​ (e) below. Assume the population is normally distributed. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). ​(c) Find the standardized test statistic t. ​(d) Decide whether to reject or fail to reject the null hypothesis. ​(e) Interpret the decision in the context of the original claim.

Answer 1

Here claim is that the mean credit card debt for individuals is greater than $ 5,000

So hypothesis is

b. The t-critical value for a right-tailed test, for a significance level of α=0.10 is

tc​=1.308

Graphically

c. Test statistics is

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

e. We have sufficient evidence to support the claim that the mean credit card debt for individuals is greater than $ 5,000