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.

Required:
Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one- tailed or two-tailed.

Answer 1

Kindly check explanation

Step-by-step explanation:

Given the following :

Sample mean (m) = 6.5

Samole standard deviation (s) = 1.5

α = 0.10

Sample size (n) = 36

μ = 6

Null : μ ≤ 6

Alternative : μ > 6

Decision region:

If Tstatistic > tα, n - 1 ; reject Null

One tailed test (right tail)

Tstatistic (t) :

(m - μ) / s/√n

(6.5 - 6) / 1.5/√36

0.5 / 0.25

= 2

tα, n - 1 = t0.1,35 ; from t table ; = 1.306

If Tstatistic > tα, n - 1 ; reject Null

2 > 1.306 ; hence reject Null