Question

A random sample of 15 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below: 44, 40, 28, 44, 28, 41, 37, 31, 43, 48, 29, 44, 45, 32, 31 Send data to Excel If we assume that the completion times are normally distributed, find a 95% confidence interval for the true mean completion time for this task. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the confidence interval?

What is the upper limit of the confidence interval?

2. A researcher collected sample data for 14 women ages 18 to 24. The sample had a mean serum cholesterol level (measured in mg/100 mL) of 189.8, with a standard deviation of 6.2. Assuming that serum cholesterol levels for women ages 18 to 24 are normally distributed, find a 90% confidence interval for the mean serum cholesterol level of all women in this age group. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the confidence interval?

What is the upper limit of the confidence interval?

Answer 1

1)

sample mean, xbar = 37.667
sample standard deviation, s = 7.118
sample size, n = 15
degrees of freedom, df = n - 1 = 14

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.145

ME = tc * s/sqrt(n)
ME = 2.145 * 7.118/sqrt(15)
ME = 3.942

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (37.667 - 2.145 * 7.118/sqrt(15) , 37.667 + 2.145 * 7.118/sqrt(15))
CI = (33.7 , 41.6)

Lower limt = 33.7
Upper limit = 41.

2)

sample mean, xbar = 189.8
sample standard deviation, s = 6.2
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.771

ME = tc * s/sqrt(n)
ME = 1.771 * 6.2/sqrt(14)
ME = 2.935

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (189.8 - 1.771 * 6.2/sqrt(14) , 189.8 + 1.771 * 6.2/sqrt(14))
CI = (186.9 , 192.7)

lower limit = 186.9
Uppe rlimit = 192.7