Question

A digital camcorder repair service has set a goal not to exceed an average of 5 working days from

the time the unit is brought in to the time repairs are completed. A random sample of 12 repair
records showed the following repair times (in days):5,6,7,7,7,5,4,6,6,5,6,7. Calculate the test statistic?

Answer 1

To calculate the test statistic for this question, follow these steps: calculate the mean repair time, calculate the sample standard deviation, calculate the standard error of the mean, and finally calculate the test statistic.

Step-by-step explanation:

To calculate the test statistic for this question, we can follow these steps:

1. Calculate the mean repair time by summing all the repair times and dividing by the sample size: (5+6+7+7+7+5+4+6+6+5+6+7)/12 = 71/12 = 5.92 days.
2. Calculate the sample standard deviation by finding the square root of the variance: √((sum of (x - mean)^2)/(sample size - 1)) = √((4.66+0.66+1.66+1.66+1.66+4.66+11.56+0.66+0.66+4.66+0.66+1.66)/11) ≈ √60.16/11 ≈ √5.47 ≈ 2.34 days.
3. Calculate the standard error of the mean by dividing the sample standard deviation by the square root of the sample size: 2.34/√12 ≈ 0.676 days.
4. Calculate the test statistic, which is the difference between the average repair time given in the question (5 days) and the mean repair time divided by the standard error of the mean: (5.92 - 5)/0.676 ≈ 1.3767.