Question

We wish to estimate the average number of heartbeats per minute for a certain population. The average number of heartbeats per minute for a sample of 64 subjects was found to be 80. Assume that these 64 patients constitute a random sample, and that the population is normally distributed with a standard deviation of 9.

(a) Construct a 95% confidence interval for µ.

(b) Find the width of a 95% confidence interval for µ.

(c) What would be the sample size needed from the same population if we want instead to have a 99% confidence interval for µ?

Suppose we want to compare the results with another population of 36 subjects whose average number of heartbeats per minute was found to be 75. Assume that these 36 patients constitute a random sample, and that the population is normally distributed with a standard deviation of 10.

(d) Construct a 95% confidence interval for µ1 − µ2, the respective population means.

Answer 1

Since , the population standard deviation is known.

Therefore , use normal distribution.

(a) Now ,

The 95% confidence interval for is ,

(b) The width of the 95% confidence interval for is ,

Width=Upper confidence limit-Lower confidence limit=82.2050-77.7950=4.41

(c)  Now ,

The margin of error is , E=width/2=4.41/2=2.2050

Therefore , the required sample size is ,

(d) The 95% confidence interval for is ,