A firm would like to know the average time its workers spend on a certain task. The...

A firm would like to know the average time its workers spend on a certain task. The firm takes a sample of 35 workers and finds that they take, on average, 13 minutes to complete the task, with a sample standard deviation of 3 minutes. Construct a 95% confidence interval for the population mean.

a) State the critical value:

b) Calculate the margin of error (round to the thousandths place):

c) State the lower and upper values of the confidence interval:

Solutions

Expert Solution

Solution :

Given that,

= 13

s =3

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 ( using student t table)

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

= 2.032* ( 3/ $\sqrt$ 35)

= 1.0304

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

- E < < + E

13- 1.0304 < < 13+ 1.0304

11.9696 < < 14.0304

( 11.9696 , 14.0304 )

orchestra answered 1 year ago

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