Question

A random sample of 46 undergraduate statistics students resulted in a sample mean age of 19.7 years, with a sample standard deviation of 3.8 years. Find the lower bound of the 90% confidence interval for the true mean age, to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 19.7

sample standard deviation = s = 3.8

sample size = n = 46

Degrees of freedom = df = n - 1 = 46 - 1 = 45

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t_0.05,45 = 1.679

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

= 1.679 * ( 3.8 / 46)

Margin of error = E = 0.9

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

- E

= 19.7 - 0.9 = 18.8

lower bound = 18.8