Question

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. Historically, the company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .10 using the critical value rule, we can show that the completion time has increased.

True

False

Answer 1

Solution:

Here, we have to use one sample t test for population mean.

Null hypothesis: H₀: The competition time has not increased.

Alternative hypothesis: H_a: The competition time has increased.

H₀: µ = 6 versus H_a: µ > 6

This is an upper tailed test. This is one tailed test.

We are given level of significance = α = 0.10

Xbar = 6.5

S = 1.5

n = 36

df = n – 1 = 35

Critical t value = 1.3062

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (6.5 – 6)/[1.5/sqrt(36)]

t = 2.0000

P-value = 0.0267

(by using t-table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the competition time has increased.

Answer: True