Question

A company claims that it has a mean customer service score of 78 (out of 100). You examine 150 customer reviews and find that the mean score of those reviews is 73 with a standard deviation of 2. Test the accuracy of the company’s claim at the 2% significance level.

Solution:

Ho: mu = 78
Ha: mu < 78 (since xbar is less than 78)
Rejection Region: qt(0.02,149); t < -2.07
Test Statistic: t = (73-78)/(2/sqrt(150)) = -30.61
In rejection region: (RHo)
P-Value Test: pt(-30.61,149) = 0%
p < alpha (RHo)
The customer value score is lower than the claimed 78.

What is wrong with this solution?

Answer 1

We will perform a two tailed test because it is not mentioned that the mean is lower or higher than population mean.

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x̅ = 73, s = 2, n = 150

Null and Alternative hypothesis:

Ho : µ = 78 (Claim)

H1 : µ ≠ 78

Test statistic:

t = (x̅ - µ)/(s/√n) = (73 - 78)/(2/√150) = -30.62

df = n-1 = 149

Critical value :

Two tailed critical value, t-crit = T.INV.2T(0.02, 149) = 2.352

Reject Ho if t < -2.352 or if t > 2.352

p-value :

Two tailed p-value = T.DIST.2T(ABS(-30.6186), 149) = 0.0000

Decision:

p-value < α, Reject the null hypothesis.

Conclusion:

There is enough evidence to reject the claim that the company has a mean customer service score of 78 at 0.02 significance level.

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If any doubt ask me in comments.