Question

Construct the 90% and 95% confidence intervals for the following data making sure to plug the numbers into the formula and show how you got all the numbers:

a. The sample mean is 22 and the population standard deviation is 2 with a sample size of 34.

b. The sample mean is 50 and the sample standard deviation is 2.5 with a sample size of 14. Assume the population is normally distributed.
Please show all work or if you used a TI 84 please explain the necessary steps to get the answer, thank you for the help :)

Answer 1

Solution:

a)

Given that,

n = 34

= 22

= 2

Note that, Population standard deviation() is known. So we use z distribution.

Use TI 84 calculator.

1) 90% confidence Interval

Press STAT

Go to TESTS menu

Go to Z Interval

Input : Data Stats

: 2

: 22

n : 34

c - Level : 0.90

Calculate

Using Out put ,

The 90% confidence interval is (21.436 , 22.564)

2)

95% confidence Interval

: 2

: 22

n : 34

c - Level : 0.95

Calculate

Using Out put ,

The 95% confidence interval is (21.328 , 22.672)

b)

Given that,

n = 14

= 50

s = 2.5

Note that, Population standard deviation() is unknown..So we use t distribution.

1) 90% confidence Interval

Press STAT

Go to TESTS menu

Go to T Interval

Input : Data Stats

: 50

sx : 2.5

n : 14

c - Level : 0.90

Calculate

Using Out put ,

The 90% confidence interval is (48.817 , 51.183)

2)

95% confidence Interval

: 50

sx : 2.5

n : 14

c - Level : 0.95

Calculate

Using Out put ,

The 95% confidence interval is (48.557 , 51.443)