Question

Use the confidence level and sample data to find a confidence interval for estimating the population mean mu. A sociologist develops a test to measure attitudes towards public transportation, and 35 randomly selected subjects are given the test . If the sample mean was 81.2 with the sample standard deviation was 24.1, construct a confidence interval to estimate the population mean if confidence level is 95%

Initial Data :

E(margin of error result value) =

Cl(population confidence inerval result value ) =

Answer 1

Solution :

Given that,

= 81.2

s = 24.1

n = 35

Degrees of freedom = df = n - 1 = 35 - 1 = 34

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,34 =2.032

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

= 2.032 * (24.1 / 35)

= 8.28

Margin of error = 8.28

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

- E < < + E

81.2 - 8.28 < < 81.2 + 8.28

72.92 < < 89.48

(72.92, 3.70 )