Question

A random sample of 16 registered nurses in a large hospital showed that they worked on average 44.7hours per week. The standard deviation of the sample was 2.2. Estimate the mean of the population with 90%confidence.Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 44.7

sample standard deviation = s = 2.2

sample size = n = 16

Degrees of freedom = df = n - 1 = 16-1=15

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.9 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,15 = 1.753

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

= 1.753 * (2.2 / 16)

E = 0.964

The 90% confidence interval estimate of the population mean is,

- E < < + E

44.7 - 0.964 < < 44.7 + 0.964

43.7 < < 45.7

(43.7 ,45.7)