Question

The pulse rates of 30 men were measured. Construct a 99% confidence interval estimate of the standard deviation.

a) 12.81 to 16.85
b) 14.62 to 18.47
c) 9.52 to 13.24
d) 11.73 to 15.69

Answer 1

To construct a 99% confidence interval estimate of the standard deviation for pulse rates of 30 men, we can use the Chi-Square distribution and find the lower and upper critical values. The confidence interval is approximately (12.81 to 16.85).

Step-by-step explanation:

To construct a confidence interval estimate of the standard deviation, we can make use of the Chi-Square distribution. In this case, since the sample size is 30, the degrees of freedom will be 29. Using the Chi-Square distribution table or a calculator, we find the lower and upper critical values for a 99% confidence level to be approximately 17.71 and 48.29. The confidence interval is then calculated as:

CI = (sqrt((n-1)*s^2)/sqrt(critical value1), sqrt((n-1)*s^2)/sqrt(critical value2))

Substituting the values, the confidence interval is (12.81 to 16.85). Therefore, option a) is correct.