Question

Assume that population mean is to be estimated from the sample described. Use the sample results to approximate the margin of error and 95% confidence interval n=49.x=63.2 seconds, s=4.5 seconds Find the 95% confidence interval _____seconds<y<____seconds (Round to one decimal place as needed)

Answer 1

Solution :

Given that,

= 63.2

s = 4.5

n = 49

Degrees of freedom = df = n - 1 = 49 - 1 = 48

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,48 =2.011

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

= 2.011 * (4.5 / 49) = 1.3

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

- E < < + E

63.2 - 1.3 < < 63.2 + 1.3

61.9 < < 64.5

61.9 seconds < y < 64.5 seconds