Question

Weight of women students at a college is believed to be normally distributed with a standard deviation of 15 ponds. To verify the claim a random sample of 36 weights from among the women students are collected and the mean was found to be 120 pounds. Find a 99% confidence interval for the true mean weight of women students at this college.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 120

sample standard deviation = s = 15

sample size = n = 36

Degrees of freedom = df = n - 1 = 35

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,35 = 2.724

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

= 2.724 * ( 15/ 36)

= 6.810

The 99% confidence interval estimate of the population mean is,

- E < < + E

120 - 6.810 < < 120 + 6.810

113.190 < < 126.810

(113.190 , 126.810)