Question

Because cardiac deaths appear to increase after heavy snowfall, an experiment was designed to compare cardiac demands of snow shoveling to use of using an electric snow thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats per minute) were recorded during both activities. The results shown below were obtained: Manual snow shoveling maximum heart rates: n = 10, xbar = 175, s = 15. Electric snow thrower maximum heart rates: n = 10, xbar = 124, s = 18. Find a 95% confidence interval estimate of the population mean for those who used the automated electric snow thrower.

A. 122 < mu < 152

B. 111 < mu  < 137

C. 109 < mu  < 143

D. 102 < mu < 142

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 124

sample standard deviation = s = 18

sample size = n = 10

Degrees of freedom = df = n - 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,9 = 2.262

Margin of error = E = t_/2,df * (s /n)

= 2.262 * ( 18/ 10)

= 12.88

The 95% confidence interval estimate of the population mean is,

- E < < + E

124 - 12.88 < < 124 + 12.88

111.12 < < 136.88

111 < < 137

Option B is correct.

Answer is 111 < < 137