Question

Assume that a sample is used to estimate a population mean μ . Find the 95% confidence interval for a sample of size 352 with a mean of 70.5 and a standard deviation of 12.6. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). < μ <

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 70.5

sample standard deviation = s = 12.6

sample size = n = 352

Degrees of freedom = df = n - 1 = 352 - 1 = 351

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,351 = 1.967

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

= 1.967 * (12.6 / 352)

Margin of error = E = 1.3

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

- E < < + E

70.5 - 1.3 < < 70.5 + 1.3

( 69.2 < < 71.8 )