Question

25 randomly selected people were surveyed and it was found that the average amount they charged was 1200 in a year with a standard deviation of 600. Given α=0.025, test the claim that the mean amount charged by all people with credit cards is greater than 1300 . Confirm your results using the p-value method as well as the critical t value.

Answer 1

To test the claim that the mean amount charged by all people with credit cards is greater than $1300, we will conduct a hypothesis test. We will use the sample mean, the population standard deviation, and the significance level to determine if there is enough evidence to support the claim.

Step-by-step explanation:

To test the claim that the mean amount charged by all people with credit cards is greater than $1300, we will conduct a hypothesis test. We will use the sample mean, the population standard deviation, and the significance level to determine if there is enough evidence to support the claim.

Hypotheses:

Null Hypothesis (H0): μ ≤ $1300

Alternative Hypothesis (Ha): μ > $1300

The test statistic for this hypothesis test is a t-score, which can be calculated using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Once we calculate the t-score, we can compare it to the critical t-value to determine if we reject or fail to reject the null hypothesis.