Question

If n=30, ¯xx¯(x-bar)=49, and s=10, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

_______< ? < ________

Answer 1

Solution :

Given that,

= 49

s = 10

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,29 = 1.699

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

= 1.699 * (10 / 30)

= 3.1

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

- E < < + E

49 - 3.1 < < 49 + 3.1

45.9 < < 52.1