Question

1. To benchmark their performance against competing healthcare institutions, a radiology center wants to know the average time taken by their staff to do an MRI test. A sample of 50 randomly selected MRI tests yielded a sample average of 47 minutes and a sample standard deviation of 9 minutes. The distribution of testing time, however, is highly skewed to the right.

   1. Suggest a plausible reason for the distribution of the MRI testing time to be right skewed.

   2. Why can one still make an inference about the average MRI testing time even though the

      distribution is skewed right?

   3. Compute a 90% confidence interval for the average MRI testing time

Answer 1

MRI testing is performed to identify any underlying disorders or disease. Some of the patients may have serious disorder/disease which require more time of MRI testing to confirm the seriousness of the complex disease. Thus, the distribution of the MRI testing time may have high extreme values and thus right skewed.

If the sample size is greater than 30, by Central Limit theorem, the distribution of average MRI testing time can be approximated by Normal distribution. Since the sample size is larger than 30, we may still make an inference about the average MRI testing time.

Since we do not know the population standard deviation, we will use t distribution to calculate 90% confidence interval for the average MRI testing time.

Degree of freedom = n - 1 = 50 - 1 = 49

Critical value of t at 90% confidence interval is 1.68

Standard error of sample mean = s / = 9 / = 1.27

Margin of error = Std error * t = 1.27 * 1.68 = 2.13

90% confidence interval for the average MRI testing time is,

(47 - 2.13, 47 + 2.13)

= (44.87 minutes, 49.13 minutes)