Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683416
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Textbook Question
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Chapter 6, Problem 6.1.1RE

The waking times (in minutes past 5:00 A.M.) of 40 people who start work at 8:00 A.M. are shown in the table at the left. Assume the population standard deviation is 45 minutes. Find (a) the point estimate of the population mean μ and (b) the margin of error for a 90% confidence interval.

(a)

Expert Solution
Check Mark
To determine

To find: The point estimate for the mean μ .

Answer to Problem 6.1.1RE

The point estimate for the mean μ is 103.5 minutes.

Explanation of Solution

Given info:

The data shows that the waking times of 40 people who start work at 8:00 A.M.

Calculation:

Point estimate:

The point estimate of the population mean μ is the sample mean (x¯) .

Software Procedure:

Step by step procedure to obtain the sample mean using the MINITAB software:

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the columns Waking times (in minutes past 5).
  • In Statistics choose mean.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: Picturing the World (7th Edition), Chapter 6, Problem 6.1.1RE , additional homework tip  1

From the MINITAB output, the point estimate for the mean waking time is 103.5 minutes.

(b)

Expert Solution
Check Mark
To determine

To find: The margin of error.

Answer to Problem 6.1.1RE

The margin of error is 11.70.

Explanation of Solution

Given info:

c=0.90 , σ=45 minutes and n=40 .

Calculation:

Critical value:

Software procedure:

Step by step procedure to obtain the P-value using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Click the Shaded Area tab.
  • Choose Probability Value and Both Tail for the region of the curve to shade.
  • Enter the Probability value as 0.10.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: Picturing the World (7th Edition), Chapter 6, Problem 6.1.1RE , additional homework tip  2

From the output, the critical value (zc) is 1.645.

Margin of error:

The formula for the margin of error is,

E=zc(σn)

Substitute 1.645 for zc , 45 for σ and 40 for n in E.

E=1.645(4540)=(1.645)(7.1151)=11.70

Thus, the margin of error is 11.70.

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Chapter 6 Solutions

Elementary Statistics: Picturing the World (7th Edition)

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