Question

1. If n=10, (x-bar)=35, and s=4, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place: __ < μ < __

2. If n=24, (x-bar)=36, and s=6, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.
Give your answers to one decimal place: __ < μ <__

3. If n=19, (x-bar)=32, and s=3, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.
Give your answers to one decimal place: __ < μ <__

Answer 1

Solution :

1.

t _/2,df = 1.833

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

= 1.833 * (4 / 10)

Margin of error = E = 2.3

The 90% confidence interval estimate of the population mean is,

- E < < + E

35 - 2.3 < < 35 + 2.3

32.7 < < 37.3

2.

t _/2,df = 1.714

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

= 1.714 * (6 / 24)

Margin of error = E = 2.1

The 90% confidence interval estimate of the population mean is,

- E < < + E

36 - 2.1 < < 36 + 2.1

33.9 < < 38.1

3.

t _/2,df = 1.734

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

= 1.734 * (3 / 19)

Margin of error = E = 1.2

The 90% confidence interval estimate of the population mean is,

- E < < + E

32 - 1.2 < < 32 + 1.2

30.8 < < 33.2