Question

50 Football Players were observed for a race. The sample mean was 30 seconds and the sample standard deviation was 2 seconds. Assuming that the population standard deviation is unknown, what is the 95% confidence interval for the population mean?

A) (26, 34)

B) (26.08, 33.92)

C) (29.446, 30.554)

D) (29.432, 30.568)

Answer 1

Solution :

Given that,

= 30

s =2

n = Degrees of freedom = df = n - 1 = 50-1 = 49

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,49 = 2.010 ( using student t table)

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

= 2.010 * (2 / 50)

= 0.568

The 95% confidence interval is,

- E < < + E

30 -0.568 < < 30 +0.568

(29.432, 30.568)