
Concept explainers
a.
Calculate the
a.

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 mean and standard deviation,
b.

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.

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.

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.

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.

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.

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.

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
- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardLet X be a continuous RV with PDF where a > 0 and 0 > 0 are parameters. verify that f-∞ /x (x)dx = 1. Find the CDF, Fx (7), of X.arrow_forward6. [20] Let X be a continuous RV with PDF 2(1), 1≤x≤2 fx(x) = 0, otherwisearrow_forward
- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03…arrow_forward
- In some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF where 1 > 0 is a parameter, and c is a constant. (a) Find the expression of c in terms of 1. (b) Find E(X). (Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)arrow_forwardSuppose that X ~Bin(n,p). Show that E[(1 - p)] = (1-p²)".arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
- I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forwardThis exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 10 grams of creatine, 39 grams of L-glutamine, and 90 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtend servings of gainzarrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_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





