Question

A farm-equipment manufacturer wants to compare the average daily downtime (in minutes) for two sheet-metal stamping machines located in two different factories. Investigation of company records for 100 randomly selected days on each of the two machines gave the following 95% confidence interval for the difference between average daily downtime in factories A and B: (1.968, 2.674).

This means:

a. 95% of the time, the difference in daily average downtime between the factories is between 1.968 minutes and 2.674 minutes.

b. There is a 95% chance that the difference in daily average downtime is between 1.968 minutes and 2.674 minutes.

c. We are 95% certain that the average daily downtime between factories is the same.

d. We are 95% certain that the average daily downtime differs between the two factories.

e. Factory A experiences downtime about twice as often as factory B.

Answer 1

b. There is a 95% chance that the difference in daily average downtime is between 1.968 minutes and 2.674 minutes.

Explanation:

The sample size for the experiment = 100

The confidence interval = 95%

The confidence interval is an estimate computed from the statistics of the observed data. The confidence interval proposes a range of possible values for an unknown parameter. The interval has an associated confidence level that the true parameter is in the proposed range.

Since the difference between the average downtime in both factories A and B is (1.968, 2.674) and the confidence interval is 95%. It means that the probability that the average downtime is between 1.968 minutes and 2.674 minutes is 0.95 i.e. 95%