Question

Use a​ t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

​Claim: μ=52,900​; α=0.10 Sample​ statistics: x=52,561​, s=2500​, n=19

Part 1:
What are the null and alternative​ hypotheses? Choose the correct answer below.
A.
H Subscript 0​: μ=52,900
H Subscript a​: μ≠52,900

B. What is the value of the standardized test​ statistic?
The standardized test statistic is

C. What is the p-value?

D. Decide whether to reject or fail to reject the null hypothesis.

Answer 1

A. The null and alternative hypotheses are:
H0: μ = 52,900
Ha: μ ≠ 52,900

B. The standardized test statistic is calculated as:
t = (x - μ) / (s / sqrt(n))
Substituting the given values, we get:
t = (52,561 - 52,900) / (2500 / sqrt(19))
t = -2.02

C. The p-value can be calculated using a t-distribution table or a calculator.

D. The decision to reject or fail to reject the null hypothesis depends on the level of significance. Since the p-value (0.059) is greater than the significance level (0.10), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the population mean is different from 52,900 at the 10% level of significance.