Question

In: Statistics and Probability

Assume that population mean is to be estimated from the sample described. Use the sample results...

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?

Solutions

Expert Solution

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


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