Question

A store owner claims the average age of her customers is 30 years. She took a survey of 33 randomly selected customers and found the average age to be 32.8 years with a standard error of 1.821. Carry out a hypothesis test to determine if her claim is valid.

(a) Which hypotheses should be tested?

H₀: p = 30 vs. H_a: p ≠ 30

H₀: μ = 30 vs. H_a: μ ≠ 30  

  H₀: μ = 30 vs. H_a: μ > 30

H₀: μ = 32.8 vs. H_a: μ ≠ 32.8

(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?

Reject the initial claim of 30 years. There is insufficient evidence the mean customer age is different than 30.

Do not reject the initial claim of 30 years. There is insufficient evidence the mean customer age is different than 30.    

Do not reject the initial claim of 30 years. There is sufficient evidence the mean customer age is different than 30.

Reject the initial claim of 30 years. There is sufficient evidence the mean customer age is different than 30.

Answer 1

Solution :

Given that,

Population mean = = 30

Sample mean = = 32.8

Population standard deviation = = 1.821

Sample size = n = 33

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

a)

Ho: 30

Ha: 30

b)

The test statistics,

Z =( - )/ (/n)

= ( 32.8 - 30 ) / ( 1.821 / 33 )

= 8.8330

c)

P- Value = 2*P(Z > z )

= 2 * 0

= 0.0000

Since, P-value < 0.05, Reject the null hypothesis.

d)

Reject the initial claim of 30 years. There is sufficient evidence the mean customer age is different than 30.