Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 10, Problem 10.1.5RE
For Exercises 1 through 7, do a complete
a. Draw the scatter plot.
b. Compute the value of the
c. Test the significance of the correlation coefficient at α = 0.01, using Table I.
d. Determine the regression line equation if r is significant.
e. Plot the regression line on the scatter plot, if appropriate.
f. Predict y′ for a specific value of x, if appropriate.
5. Typing Speed and Word Processing A researcher desires to know whether the typing speed of a secretary (in words per minute) is related to the time (in hours) that it takes the secretary to learn to use a new word processing program. The data are shown.
If there is a significant relationship, predict the time it will take the average secretary who has a typing speed of 72 words per minute to learn the word processing program. (This information will be used for Exercises 9 and 11.)
a.
Expert Solution
To determine
To construct: The scatterplot for the variablesthe speed and time.
Answer to Problem 10.1.5RE
Output using the MINITAB software is given below:
Explanation of Solution
Given info:
The data shows the typing speed of a secretary (in words per minute) (x) and the time (in hours) (y) values.
Calculation:
Step by step procedure to obtain scatterplot using the MINITAB software:
- Choose Graph > Scatterplot.
- Choose Simple and then click OK.
- Under Y variables, enter a column ofTime.
- Under X variables, enter a column ofSpeed.
- Click OK.
b.
Expert Solution
To determine
To compute: The value of the correlation coefficient.
Answer to Problem 10.1.5RE
The value of the correlation coefficientis –0.974.
Explanation of Solution
Calculation:
Correlation coefficient r:
Software Procedure:
Step-by-step procedure to obtain the ‘correlation coefficient’ using the MINITAB software:
- Select Stat >Basic Statistics > Correlation.
- In Variables, select x and y from the box on the left.
- Click OK.
Output using the MINITAB software is given below:
From the MINITAB output, the value of the correlation is –0.974.
c.
Expert Solution
To determine
To test: The significance of the correlation coefficient at
Answer to Problem 10.1.5RE
The conclusion is that,there is a linear relation between the speed and time.
Explanation of Solution
Given info:
The level of significance is
Calculation:
The hypotheses are given below:
Null hypothesis:
That is, there is no linear relation betweenthe speed and time.
Alternative hypothesis:
That is, there is a linear relation between the speed and time.
The sample size is 12.
The formula to find the degrees of the freedom is
That is,
From the “TABLE –I: Critical Values for the PPMC”, the critical value for 10 degrees of freedom and
Rejection Rule:
If the absolute value of r is greater than the critical value then reject the null hypothesis.
Conclusion:
From part (b), the value of r is–0.974that is the absolute value of r is 0.974.
Here, the absolute value of r is greater than the critical value
That is,
By the rejection rule,reject the null hypothesis.
There is asufficient evidence to support the claim that “there is alinear relation betweenthespeed and time.
d.
Expert Solution
To determine
To find: The regression equation for the given data.
Answer to Problem 10.1.5RE
The regression equation for the given datais
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to obtain the regression equation using the MINITAB software:
- Choose Stat > Regression > Regression.
- In Responses, enter the column ofTime.
- In Predictors, enter the column ofSpeed.
- Click OK.
Output using the MINITAB software is given below:
Thus, regression equation for the given datais
e.
Expert Solution
To determine
To construct: The scatterplot for the variablesthe speed and time with regression line.
Answer to Problem 10.1.5RE
Output using the MINITAB software is given below:
Explanation of Solution
Calculation:
Step by step procedure to obtain scatterplot using the MINITAB software:
- Choose Graph > Scatterplot.
- Choose with line and then click OK.
- Under Y variables, enter a column of Time.
- Under X variables, enter a column ofSpeed.
- Click OK.
f.
Expert Solution
To determine
To obtain: The predicted value of the time with speed of 72 words perminute.
Answer to Problem 10.1.5RE
Thepredicted value of the time is 4.726.
Explanation of Solution
Calculation:
Thus, regression equation for the given datais
Substitute x as 72 in the regression equation
Thus, the predicted value of the time is 4.726.
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Students have asked these similar questions
Use the following data to:
a) determine the correlation coefficient, rounded to the nearest thousandth
b) find the equation of the regression line for time watching tv and time on the internet
c) approximate how much time on the internet can we predict for a person who spends 10 hours weekly watching tv.
subject
A
B
C
D
E
F
G
Watching tv
8
4
2
7
7
5
6
Time on the internet
14
12
8
17
18
9
18
Use the following data to a. determine the coefficient of correlation, rounded to the nearest thousandth, b. find the equation of the regression line for time watching TV and time on the Internet, c. approximate how much time on the Internet can we predict for a person who spends 10 hours weekly watching TV.Subject: A B C D E F GTime watching TV: 8, 4, 2, 7, 7, 5, 6Time on the internet: 14, 12, 8, 17, 18, 9, 18
A. a. r = 0.752 b. y = 1.52x + 5.25 c. 20.5 hours
B. a. r = -0.752 b. y = -1.52x + 5.25 c. 9.9 hours
C. a. r = -0.752 b. y = 5.25x + 1.52 c. 54 hours
D. a. r = 0.752 b. y = 1.52x - 5.25 c. 10 hours
Which of the following denotes the slope or the regression coefficient for X?
A) The term a
B) The term b
C) The error term
D) The correlation coefficient, r
Chapter 10 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 10.1 - Stopping Distances In a study on speed control, it...Ch. 10.1 - What is meant by the statement that two variables...Ch. 10.1 - How is a linear relationship between two variables...Ch. 10.1 - What is the symbol for the sample correlation...Ch. 10.1 - What is the range of values for the correlation...Ch. 10.1 - What is meant when the relationship between the...Ch. 10.1 - Give examples of two variables that are positively...Ch. 10.1 - What is the diagram of the independent and...Ch. 10.1 - What is the name of the correlation coefficient...Ch. 10.1 - What statistical test is used to test the...
Ch. 10.1 - When two variables are correlated, can the...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 23ECh. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECCh. 10.1 - Prob. 29ECCh. 10.1 - Prob. 30ECCh. 10.2 - Applying the Concepts 102 Stopping Distances...Ch. 10.2 - What two things should be done before one performs...Ch. 10.2 - What are the assumptions for regression analysis?Ch. 10.2 - Prob. 3ECh. 10.2 - What is the symbol for the slope? 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How is...Ch. 10.3 - What is meant by the unexplained variation? How is...Ch. 10.3 - What is meant by the total variation? How is it...Ch. 10.3 - Define the coefficient of determination.Ch. 10.3 - How is the coefficient of determination found?Ch. 10.3 - Define the coefficient of nondetermination.Ch. 10.3 - How is the coefficient of nondetermination found?Ch. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Compute the standard error of the estimate for...Ch. 10.3 - Compute the standard error of the estimate for...Ch. 10.3 - Compute the standard error of the estimate for...Ch. 10.3 - Prob. 19ECh. 10.3 - For the data in Exercises 14 in Sections 101 and...Ch. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.4 - Applying the Concepts 104 More Math Means More...Ch. 10.4 - Explain the similarities and differences between...Ch. 10.4 - What is the general form of the multiple...Ch. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - How do the values of the individual correlation...Ch. 10.4 - Age, GPA, and Income A researcher has determined...Ch. 10.4 - Nursing Home Satisfaction A researcher found that...Ch. 10.4 - Special Occasion Cakes A pastry chef who...Ch. 10.4 - Aspects of Students Academic Behavior A college...Ch. 10.4 - Age, Cholesterol, and Sodium A medical researcher...Ch. 10.4 - Explain the meaning of the multiple correlation...Ch. 10.4 - What is the range of values R can assume?Ch. 10.4 - Prob. 13ECh. 10.4 - What are the hypotheses used to test the...Ch. 10.4 - What test is used to test the significance of R?Ch. 10.4 - What is the meaning of the adjusted R2? 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Find R when ryx1 = 0.561 and ryx2 = 0.714...Ch. 10 - Prob. 28CQCh. 10 - Prob. 1CTCCh. 10 - Prob. 2CTCCh. 10 - Prob. 3CTCCh. 10 - Prob. 4CTCCh. 10 - Product Sales When the points in a scatter plot...Ch. 10 - Prob. 6CTCCh. 10 - Prob. 7CTCCh. 10 - Product Sales When the points in a scatter plot...Ch. 10 - Prob. 9CTC
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