Question

According to a study done by Dr. Martha S. Linet and others, the mean duration of the most recent headache was 8.2 hours for a sample of 5055 females 12 through 29. Make a 95% confidence interval for the mean duration of all headaches for all 12 to 29-year-old females. The standard deviation for this sample is 2.4 hours.

Answer 1

Solution :

sample size = n = 5055

Degrees of freedom = df = n - 1 = 5054

t /2,df = 1.96

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

= 1.96 * (2.4 / 5055)

Margin of error = E = 0.1

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

- E < < + E

8.2 - 0.1 < < 8.2 + 0.1

8.1 < < 8.3

(8.1, 8.3)