Question

A store owner claims the average age of her customers is 28 years. She took a survey of 38 randomly selected customers and found the average age to be 29.7 years with a standard error of 1.180. Carry out a hypothesis test to determine if her claim is valid.

(a) Which hypotheses should be tested?

- H₀: μ = 28 vs. H_a: μ > 28

- H₀: μ = 29.7 vs. H_a: μ ≠ 29.7     

- H₀: μ = 28 vs. H_a: μ ≠ 28

- H₀: p = 28 vs. H_a: p ≠ 28

(b) Find the test statistic:  (Use 4 decimals.)

(c) What is the P-value?  (Use 4 decimals.)

(d) What should the store owner conclude, for α = 0.05?

- Do not reject the initial claim of 28 years. There is sufficient evidence the mean customer age is different than 28.

- Do not reject the initial claim of 28 years. There is insufficient evidence the mean customer age is different than 28.     

- Reject the initial claim of 28 years. There is sufficient evidence the mean customer age is different than 28.

- Reject the initial claim of 28 years. There is insufficient evidence the mean customer age is different than 28.

(e) If mean customer age really is equal to 30.8 years, but you conclude it is equal to 28 years, which type of error did you make, if any?

- Type II error

- The p-value is correct; therefore no error was made     

- Both Type I and Type II error

- Type I error

Answer 1