Company A is considering replacing a specialized machine that is thought to have

Question

Company A is considering replacing a specialized machine that is thought to have an excessive repair time. The repair time was collected from 15 randomly selected machines, which were found to have a mean repair time of 86 hours with a standard deviation of 29 hours.

A) What are the appropriate hypotheses for this experiment? (for 80 hours)

B) We want to test to see if there is sufficient evidence to suggest that the repair time for this series of machines exceeds 80 hours using a significance level of 0.05. What is the observed value of the test statistic?

C) What is the critical value for the test statistic?

D) Do we reject or fail to reject the null hypothesis?

E) Construct a 95% confidence interval for this test. What is the lower limit of this interval?

Explanation / Answer

Here sample size = n = 15
sample mean = 86 hours, sample sd = 29 hours

A) Null hypothesis = The repair time of machines is less than or equal to 80 hours
Alternative hypothesis = The repair time of machines is greater than 80 hours
This is one tailed t test.

B) Standard error = sd/sqrt(n) = 29/sqrt(15) = 7.487768
Degrees of freedom = n - 1 = 15 - 1 = 14
t statistic = (86 - 80)/7.487768 = 0.8013069

C) Here significance level = 0.05
So critical probability = 1 - 0.05/2 = 0.975
Degrees of freedom = 14

Now Critical value of the test statistic can be found out using the t table, which is 2.145

D) Since the test statistic value 0.8013069 is lesser than the critical value of 2.145, we fail to reject the null hypothesis.

E) First we need to find the margin of error.
Margin of error = critical value * standard error = 2.145 * 7.487768 = 16.06126

Confidence interval = sample statistic +- margin of error
= 86 +- 16.06126

So confidence interval is from (86 - 4.98453) to (86 + 4.98453) = (69.93874,102.0613)

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