Final answer:
The claim cannot be supported as the test statistic is less than the critical value, therefore failing to reject the null hypothesis.
Step-by-step explanation:
(a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha?
The claim can be written mathematically as H0: μ ≤ $5,000 and Ha: μ > $5,000.
(b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), t0?
Since the sample size is greater than 30 and assuming the population is normally distributed, we can use a t-distribution with degrees of freedom equal to n-1. At α=0.05 and degrees of freedom 34, the critical value t0 is approximately 1.690.
(c) Find the standardized test statistic t.
The standardized test statistic t is calculated as t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, t = (5160 - 5000) / (625 / sqrt(35)), which is approximately 1.04.
(d) Decide whether to reject or fail to reject the null hypothesis.
Compare the test statistic t to the critical value t0. If t > t0, reject the null hypothesis; otherwise, fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
Based on the test, since the test statistic t (1.04) is less than the critical value t0 (1.690), we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that the mean credit card debt for individuals is greater than $5,000.