![Essential Statistics](https://www.bartleby.com/isbn_cover_images/9781259570643/9781259570643_largeCoverImage.gif)
Concept explainers
a.
Calculate the
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The correlation between math score and verbal SAT score is 0.75.
Explanation of Solution
Calculation:
The verbal SAT scores (x) and the math SAT scores (y) of six fishermen are given.
Correlation:
The
Software procedure:
Step-by-step procedure to obtain the correlation using the MINITAB software:
- Choose Stat > Basic Statistics > Correlation.
- In Variables, enter the columns of x and y.
- Click OK.
Output using the MINITAB software is given below:
Hence, the correlation between math score and verbal SAT score is 0.75.
b.
Calculate the
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The mean,
The standard deviation,
Explanation of Solution
Calculation:
Denote
Software procedure:
Step-by-step procedure to obtain the descriptive statistics using the MINITAB software:
- Choose Stat > Basic Statistics > Display Descriptive Statistics, click OK.
- In Variables, enter the columns of x.
- Choose Statistics, select Mean, Standard deviation and click OK.
- Click OK.
Output using the MINITAB software is given below:
From the above output, it is evident that the mean,
c.
Calculate the mean and standard deviation,
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The mean,
The standard deviation,
Explanation of Solution
Calculation:
Denote
Descriptive statistics:
Software procedure:
Step-by-step procedure to obtain the descriptive statistics using the MINITAB software:
- Choose Stat > Basic Statistics > Display Descriptive Statistics, click OK.
- In Variables, enter the columns of y.
- Choose Statistics, select Mean, Standard deviation and click OK.
- Click OK.
Output using the MINITAB software is given below:
From the above output, it is evident that the mean,
d.
Find the least-squares regression line to predict the math score from the verbal score.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The least-squares regression line to predict the math score from the verbal score is
Explanation of Solution
Calculation:
Least-squares regression:
For an ordered pairs of values of variables, (x, y) with respective means
Regression:
Software procedure:
Step by step procedure to obtain regression using Minitab software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- In Responses, enter the numeric column containing the response data y.
- In Continuous Predictors, enter the numeric column containing the predictor variable x.
- Choose Results, select Regression equation and click OK.
- Click OK.
Output using MINITAB software is given below:
From the output, the least-squares regression line to predict the math score from the verbal score is
e.
Find the z-score for each value of x.
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The z-scores for the values of x are:
0.0324 |
–0.3082 |
1.8573 |
–0.8759 |
0.1135 |
–0.8191 |
Explanation of Solution
Calculation:
The z-score for an x-value is denoted as
Here,
The calculation for the z-scores for the values of x is shown in the following table:
x | ||
428 | 4 | 0.0324 |
386 | –38 | –0.3082 |
653 | 229 | 1.8573 |
316 | –108 | –0.8759 |
438 | 14 | 0.1135 |
323 | –101 | –0.8191 |
f.
Find the z-score for each value of y.
f.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The z-score for the values of y are:
–0.8777 |
0.4983 |
1.2974 |
–1.2530 |
0.7484 |
–0.4121 |
Explanation of Solution
Calculation:
The z-score for a y-value is denoted as
Here,
The calculation for the z-scores for the values of y is shown in the following table:
y | ||
373 | –126.3 | –0.8777 |
571 | 71.7 | 0.4983 |
686 | 186.7 | 1.2974 |
319 | –180.3 | –1.2530 |
607 | 107.7 | 0.7484 |
440 | –59.3 | –0.4121 |
g.
Find the correlation coefficient, r, between
Explain whether this correlation is the same as the correlation between math and verbal SAT scores.
g.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The correlation, r, between
The correlation between
Explanation of Solution
Calculation:
Correlation:
Software procedure:
Step-by-step procedure to obtain the correlation using the MINITAB software:
- Choose Stat > Basic Statistics > Correlation.
- In Variables, enter the columns of zx and zy.
- Click OK.
Output using the MINITAB software is given below:
Hence, the correlation, r, between
Observe that the correlation between math and verbal SAT scores obtained in part a is 0.75.
Hence, the correlation between
h.
Find the least-squares regression line to predict
Explain the reason the equation of the line is
h.
![Check Mark](/static/check-mark.png)
Answer to Problem 35E
The least-squares regression line to predict
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to obtain regression using Minitab software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- In Responses, enter the numeric column containing the response data zy.
- In Continuous Predictors, enter the numeric column containing the predictor variable zx.
- Choose Results, select Regression equation and click OK.
- Click OK.
Output using MINITAB software is given below:
From the output, the least-squares regression line obtained is:
Hence, the least-squares regression line to predict
Consider the least-squares regression equation:
Now,
Here,
Now, in terms of
Hence, the equation of the line in terms of
Want to see more full solutions like this?
Chapter 11 Solutions
Essential Statistics
- Suppose that the chance that an elementary student eats hot lunch is 30 percent. What’s the chance that, among 20 randomly selected students, between 6 and 8 students eat hot lunch (inclusive)?arrow_forwardBob’s commuting times to work are varied. He makes it to work on time 80 percent of the time. On 12 randomly selected trips to work, what’s the chance that Bob makes it on time at least 10 times?arrow_forwardYour chance of winning a small prize in a scratch-off ticket is 10 percent. You buy five tickets. What’s the chance you will win at least one prize?arrow_forward
- Suppose that 60 percent of families own a pet. You randomly sample four families. What is the chance that two or three of them own a pet?arrow_forwardIf 40 percent of university students purchase their textbooks online, in a random sample of five students, what’s the chance that exactly one of them purchased their textbooks online?arrow_forwardA stoplight is green 40 percent of the time. If you stop at this light eight random times, what is the chance that it’s green exactly five times?arrow_forward
- If 10 percent of the parts made by a certain company are defective and have to be remade, what is the chance that a random sample of four parts has one that is defective?arrow_forwardQuestion 4 Fourteen individuals were given a complex puzzle to complete. The times in seconds was recorded for their first and second attempts and the results provided below: 1 2 3 first attempt 172 255 second attempt 70 4 5 114 248 218 194 270 267 66 6 7 230 219 341 174 8 10 9 210 261 347 218 200 281 199 308 268 243 236 300 11 12 13 14 140 302 a. Calculate a 95% confidence interval for the mean time taken by each individual to complete the (i) first attempt and (ii) second attempt. [la] b. Test the hypothesis that the difference between the two mean times for both is 100 seconds. Use the 5% level of significance. c. Subsequently, it was learnt that the times for the second attempt were incorrecly recorded and that each of the values is 50 seconds too large. What, if any, difference does this make to the results of the test done in part (b)? Show all steps for the hypothesis testarrow_forwardQuestion 3 3200 students were asked about the importance of study groups in successfully completing their courses. They were asked to provide their current majors as well as their opinion. The results are given below: Major Opinion Psychology Sociology Economics Statistics Accounting Total Agree 144 183 201 271 251 1050 Disagree 230 233 254 227 218 1162 Impartial 201 181 196 234 176 988 Total 575 597 651 732 645 3200 a. State both the null and alternative hypotheses. b. Provide the decision rule for making this decision. Use an alpha level of 5%. c. Show all of the work necessary to calculate the appropriate statistic. | d. What conclusion are you allowed to draw? c. Would your conclusion change at the 10% level of significance? f. Confirm test results in part (c) using JASP. Note: All JASP input files and output tables should be providedarrow_forward
- Question 1 A tech company has acknowledged the importance of having records of all meetings conducted. The meetings are very fast paced and requires equipment that is able to capture the information in the shortest possible time. There are two options, using a typewriter or a word processor. Fifteen administrative assistants are selected and the amount of typing time in hours was recorded. The results are given below: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 typewriter 8.0 6.5 5.0 6.7 7.8 8.5 7.2 5.7 9.2 5.7 6.5 word processor 7.2 5.7 8.3 7.5 9.2 7.2 6.5 7.0 6.9 34 7.0 6.9 8.8 6.7 8.8 9.4 8.6 5.5 7.2 8.4 a. Test the hypothesis that the mean typing time in hours for typewriters is less than 7.0. Use the 1% level of significance. b. Construct a 90% confidence interval for the difference in mean typing time in hours, where a difference is equal to the typing time in hours of word processors minus typing time in hours of typewriter. c. Using the 5% significance level, determine whether there is…arrow_forwardIllustrate 2/7×4/5 using a rectangular region. Explain your work. arrow_forwardWrite three other different proportions equivalent to the following using the same values as in the given proportion 3 foot over 1 yard equals X feet over 5 yardsarrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
![Text book image](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)