Question

In: Statistics and Probability

Straight glass- mean: 7.987; standard deviation: 2.459; n: 10 Curved glass- mean: 6.930. standard deviation: 3.748;...

Straight glass- mean: 7.987; standard deviation: 2.459; n: 10

Curved glass- mean: 6.930. standard deviation: 3.748; n: 10

What is the 95% confidence interval?

Expert Solution

Solution :

Given that,

= 7.987

s = 2.459

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,9 = 2.262

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.262 * (2.459 / $\sqrt$ 10)

= 1.759

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

- E < < + E

7.987 - 1.759 < < 7.987 + 1.759

6.228 < < 9.746

(6.228,9.746)

The 95% confidence interval is 6.228 to 9.746

Given that,

= 6.930

s = 3.748

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,9 = 2.262

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.262 * (3.748 / $\sqrt$ 10)

= 2.681

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

- E < < + E

6.930 - 2.681 < < 6.930 + 2.681

4.249 < < 9.611

(4.249,9.611)

The 95% confidence interval is 4.249 to 9.611

orchestra answered 1 year ago

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