Question

In: Statistics and Probability

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

1. 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:

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)

= 1.030

The 95% confidence interval is,

- E < < + E

13 - 1.030< <13 +1.030

11.970 < < 14.030

(11.970 , 14.030)

orchestra answered 3 years ago

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