Question

You are interested in finding a 98% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 14 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.

19 27 27 20 17 6 23 25 7 24 20 25 18 24

a. To compute the confidence interval use a distribution.

b. With 98% confidence the population mean number of visits per physical therapy patient is between BLANK and BLANK visits.

c. If many groups of 14 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About BLANK percent of these confidence intervals will contain the true population mean number of visits per patient and about BLANK percent will not contain the true population mean number of visits per patient.

Answer 1

Values are given as,

19 ,27 ,27 ,20, 17, 6, 23, 25, 7 ,24, 20, 25 ,18 ,24

Using excel function to find the mean and standard deviation:

Function =AVERAGE (19 ,27 ,27 ,20, 17, 6, 23, 25, 7 ,24, 20, 25 ,18 ,24 ) , we get   = 20.14

Function =STDEV.S (19 ,27 ,27 ,20, 17, 6, 23, 25, 7 ,24, 20, 25 ,18 ,24 ) , we get   s= 6.6084

A) Calculating 98%  confidence interval :

Values are given as,

Mean, x bar = 20.14,
Sample Standard Deviation, s = 6.6084,
Sample Size, n = 14,

Degree of freedom, df = n - 1 = 13,
alpha = 1 - (98/100) = 0.020,

Using df = 13 and alpha = 0.020 in t Table,
t = 2.65
Now, using the formula


Put the values in the above formula:

= 15.4597, 24.8203

The 98% Confidence Interval = [15.460, 24.820]

B) Interpretation: With 98% confidence the population mean number of visits per physical therapy patient is between 15.460 and 24.820 visits.

C) . If many groups of 14 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About 98   percent of these confidence intervals will contain the true population mean number of visits per patient and about 2 percent will not contain the true population mean number of visits per patient.