Question

A computer repair center advertises that it will solve any computer problem in less than 5 days. A sample of 25 past repairs yielded a mean repair time of 4.6 days and a standard deviation of 1.05 days. Assume that the repair times are normally distributed. Test to determine if their advertisement is legitimate at 5% significance level. (Show all steps)

Answer 1

ANSWER::

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 5
Alternative Hypothesis, Ha: μ < 5

Rejection Region
This is left tailed test, for α = 0.05 and df = 24
Critical value of t is -1.711.
Hence reject H0 if t < -1.711

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.6 - 5)/(1.05/sqrt(25))
t = -1.9

P-value Approach
P-value = 0.0348
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the repair time is less than 5 days.

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