Question

The following data set represents the average number of minutes played for a random sample of professional basketball players in a recent season.

35.9        33.8          34.7          31.5          33.2        29.1          30.7          31.2 36.1          34.9

a) Find the sample mean and sample standard deviation
b) Construct a 90% confidence interval for the population mean and interpret the results. Assume the population is normally distributed.
c) Calculate the two standard deviation interval and discuss the difference in meaning from it and the confidence interval from part a.

Answer 1

Here in this scenario to compute the Confidence Interval for population mean we need to use t distribution because here the population standard deviations is unknown.

Further the computation of Confidence Interval with appropriate steps as below,

a) The sample mean is 33.11 and sample Standerd deviation is 2.382.

The t critical value is calculated using t table or using Excel.

c) the 90% Confidence Interval for population Standerd deviation is calculated using chi square distribution as below,

Now, we need to square all the sample values as shown in the table below:

Observation:	X	X^2
1	35.9	1288.81
2	33.8	1142.44
3	34.7	1204.09
4	31.5	992.25
5	33.2	1102.24
6	29.1	846.81
7	30.7	942.49
8	31.2	973.44
9	36.1	1303.21
10	34.9	1218.01
Sum =	331.1	11013.79

Therefore, the sample variance is computed as shown below:

The chi square critical value is calculated using chi square table or using Excel.

The main difference between part B and part C is that in part B we calculated the 90% Confidence Interval for population mean and in part c we computed the 90% Confidence Interval for population Variance and Standerd deviation.

Thank you.