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=36, x=61.2 ​seconds, s=4.14 seconds

Margin of error is 1.4 seconds, what is the 95% confidence interval?

? seconds <μ< ? seconds?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 61.2

sample standard deviation = s = 4.14

sample size = n = 36

Degrees of freedom = df = n - 1 = 36-1= 35

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,35 = 2.030

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

= 2.030 * (4.14 / 36)

E = 1.4

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

- E < < + E

61.2 - 1.4 < < 61.2 + 1.4

59.8 < < 62.6

(59.8,62.6)

The 95% confidence interval is

59.8 Seconds < < 62.6 seconds