Question

Consumer Reports uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of σ = 12 is expected. In 2012, Costco, with its 432 warehouses in 40 states, was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Costco customer satisfaction scores follows.

95	90	83	75	95
98	80	83	82	93
86	80	94	64	62

(a)What is the sample mean customer satisfaction score for Costco?

(b)What is the sample variance? (Round your answer to two decimal places.)

(c)What is the sample standard deviation? (Round your answer to two decimal places.)

(d )Construct a hypothesis test to determine whether the population standard deviation of σ = 12

should be rejected for Costco. With a 0.05 level of significance, what is your conclusion?

State the null and alternative hypotheses.

a) H₀: σ² > 144

H_a: σ² ≤ 144

b) H₀: σ² ≥ 144

H_a: σ² < 144    

c) H₀: σ² ≤ 144

H_a: σ² > 144

d) H₀: σ² = 144

H_a: σ² ≠ 144

e) H₀: σ² < 144

H_a: σ² ≥ 144

Find the value of the test statistic. (Round your answer to three decimal places.)

test statistic=

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We can conclude that the population standard deviation is not 12.

Reject H₀. We cannot conclude that the population standard deviation is not 12.   

Do not reject H₀. We can conclude that the population standard deviation is not 12.

Do not reject H₀. We cannot conclude that the population standard deviation is not 12.

Answer 1