Question

A study of 45 students revealed that they drank an average of 2.1 cups of coffee each day, and the sample standard deviation was found to be 1.1 cups of coffee. (a) Construct a 99% confidence interval for the average number of cups of coffee a college student drinks each day. (b) Construct a one-sided 98% confidence interval with a left endpoint for the average number of cups of coffee a college student drinks each day.

Answer 1

Solution :

Given that,

= 2.1 cups

s = 1.1 cups

n = 45

Degrees of freedom = df = n - 1 = 45 - 1 = 44

a ) At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,44 =2.692

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

= 2.692 * ( 1.1 / 45)

= 0.44

The 99% confidence interval estimate of the population mean is,

- E < < + E

2.1 - 0.44< < 21.1 + 0.44

1.66 < < 2.54

(1.66, 2.54 )

b ) At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t _/2,df = t_0.01,44 = 2.414

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

= 2.414 * ( 1.1  / 45)

= 0.40

The 98% confidence interval estimate of the population mean is,

- E < < + E

- E

2.1 - 0.40 = 1.7

Left endpoint = 1.7