Question

Use the standard normal distribution or the​ t-distribution to construct a 95​% confidence interval for the population mean. Justify your decision. If neither distribution can be ​used, explain why. Interpret the results. In a random sample of 47 people, the mean body mass index​ (BMI) was 27.7 and the standard deviation was 6.02. Which distribution should be used to construct the confidence ​interval? Choose the correct answer below:

Answer 1

Solution :

Using t distribution ,

Given that,

= 27.7

s = 6.02

n = 47

Degrees of freedom = df = n - 1 = 47 - 1 = 46

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,46 = 2.013

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

= 2.013 * (6.02 / 47)

= 1.77

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

- E < < + E

27.7 - 1.77 < < 27.7 - 1.77

25.93 < < 29.47

(25.93 , 29.47)