Question

n = 1337 x¯= 15.73. s = 2.57 Compute a 95% confidence interval for the population mean.

a) We have 95% confidence that the interval 15.67≤μ≤ 15.79 will contain the population mean.

b) We have 95% confidence that the interval 15.68≤μ≤ 15.78 will contain the population mean.

c) We have 95% confidence that the interval, 15.59 ≤ μ ≤ 15.87, will contain the population mean.

d) We have 95% confidence that the interval 13.77≤μ≤ 17.69 will contain the population mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.73

sample standard deviation = s = 2.57

sample size = n = 1337

Degrees of freedom = df = n - 1 = 1337 - 1 = 1336

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,1336 = 1.962

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

= 1.962 * (2.57 / 1337)

= 0.14

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

- E < < + E

15.73 - 0.14 < < 15.73 + 0.14

15.59 < < 15.87

c) We have 95% confidence that the interval, 15.59 ≤ μ ≤ 15.87, will contain the population mean.