Question

 

A random sample of 10 children found that their average growth for the first year was 9.8 inches with a sample standard deviation of 0.96 inches. Use this information to calculate a 95% confidence interval for the mean growth of all children during the first year. Use your graphing calculator.

12. Enter the value of the lower end of this confidence interval.

13. Enter the value of the upper end of this confidence interval.

Answer 1

 

= 9.8

s = 0.96

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 /√n)

= 2.262 * (0.96 / √10)

= 0.7

Margin of error = 0.7

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

- E < < + E

9.8 - 0.7< < 9.8 + 0.7

9.1 < < 10.5

The lower value = 9.1

The upper vallue =10.5