Question

We want to know how many hours per week, on average, mothers spend with their preschool children. We draw a random sample of 300 mothers and find x bar=50.32 hours and s = 10.27 hours. What is the interval within which, with 95% confidence, the true mean number of hours a week all mothers spend with their preschool children falls? Please interpret this confidence interval too.

Answer 1

Solution :

Given that,

= 50.32

s = 10.27

n = 300

Degrees of freedom = df = n - 1 = 300 - 1 = 299

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,299 =1.968

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

= 1.968 * ( 10.27 / 300)

= 1.17

Margin of error = 1.17

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

- E < < + E

50.32 - 1.17 < < 50.32 + 1.17

49.15 < < 51.49

(49.15, 51.49 )