(a)
Construct a
(a)

Answer to Problem 9P
The scatter diagram for data is,
Explanation of Solution
Calculation:
The variable x denotes the weight of the car (in hundreds of pounds) and y denotes the miles per gallon (mpg).
Step by step procedure to obtain scatter plot using MINITAB software is given below:
- Choose Graph > Scatterplot.
- Choose Simple. Click OK.
- In Y variables, enter the column of x.
- In X variables, enter the column of y.
- Click OK.
(b)
Verify the values of
(b)

Explanation of Solution
Calculation:
The formula for
In the formula, n is the
The values are verified in the table below,
x | y | xy | ||
27 | 30 | 729 | 900 | 810 |
44 | 19 | 1936 | 361 | 836 |
32 | 24 | 1024 | 576 | 768 |
47 | 13 | 2209 | 169 | 611 |
23 | 29 | 529 | 841 | 667 |
40 | 17 | 1600 | 289 | 680 |
34 | 21 | 1156 | 441 | 714 |
52 | 14 | 2704 | 196 | 728 |
Hence, the values are verified.
The number of data pairs are
Hence, the value of r is verified as approximately –0.946.
(c)
Find the value of
Find the value of
Find the value of a.
Find the value of b.
Find the equation of the least-squares line.
(c)

Answer to Problem 9P
The value of
The value of
The value of a is 43.326.
The value of b is –0.6007.
The equation of the least-squares line is
Explanation of Solution
Calculation:
From part (b), the values are
The value of
Hence, the value of
The value of
Hence, the value of
The value of b is,
Hence, the value of b is –0.6007.
The value of a is,
Hence, the value of a is 43.326.
The equation of the least-squares line is,
Hence, the equation of the least-squares line is
(d)
Construct a scatter diagram with least squares line.
Locate the point
(d)

Answer to Problem 9P
The scatter diagram with least squares line with point
Explanation of Solution
Calculation:
In the dataset of eight weights and miles per gallon also include the point
Step by step procedure to obtain scatter plot using MINITAB software is given below:
- Choose Graph > Scatterplot.
- Choose With regression. Click OK.
- In Y variables, enter the column of x.
- In X variables, enter the column of y.
- Click OK.
(e)
Find the value of the coefficient of determination
Mention percentage of the variation in y that can be explained by variation in x.
Mention percentage of the variation in y that cannot be explained by variation in x.
(e)

Answer to Problem 9P
The value of the coefficient of determination
The percentage of the variation in y that can be explained by variation in x is 89.4%.
The percentage of the variation in y that cannot be explained by variation in x is 10.6%.
Explanation of Solution
Calculation:
Coefficient of determination
The coefficient of determination
From part (b), the value of
Hence, the value of the coefficient of determination
About 89.4% of the variation in y (miles per gallon (mpg)) is explained by x (weight of the car (in hundreds of pounds)). Since the value of
Hence, the percentage of the variation in y that can be explained by variation in x is 89.4%.
About 10.6%
Hence, the percentage of the variation in y that cannot be explained by variation in x is 10.6%.
(f)
Find the number of miles per gallon for car weight
(f)

Answer to Problem 9P
The number of miles per gallon for car weight
Explanation of Solution
Calculation:
From part (c), the equation of the least-squares line is
Substitute
Hence, the number of miles per gallon for car weight
Want to see more full solutions like this?
Chapter 9 Solutions
UNDERSTANDABLE STAT. >PRINT UPGRADE<
- A researcher wishes to estimate, with 90% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 4% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 65% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b). ... (a) What is the minimum sample size needed assuming that no prior information is available? n = (Round up to the nearest whole number as needed.)arrow_forwardThe table available below shows the costs per mile (in cents) for a sample of automobiles. At a = 0.05, can you conclude that at least one mean cost per mile is different from the others? Click on the icon to view the data table. Let Hss, HMS, HLS, Hsuv and Hмy represent the mean costs per mile for small sedans, medium sedans, large sedans, SUV 4WDs, and minivans respectively. What are the hypotheses for this test? OA. Ho: Not all the means are equal. Ha Hss HMS HLS HSUV HMV B. Ho Hss HMS HLS HSUV = μMV Ha: Hss *HMS *HLS*HSUV * HMV C. Ho Hss HMS HLS HSUV =μMV = = H: Not all the means are equal. D. Ho Hss HMS HLS HSUV HMV Ha Hss HMS HLS =HSUV = HMVarrow_forwardQuestion: A company launches two different marketing campaigns to promote the same product in two different regions. After one month, the company collects the sales data (in units sold) from both regions to compare the effectiveness of the campaigns. The company wants to determine whether there is a significant difference in the mean sales between the two regions. Perform a two sample T-test You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. (2 points = 0.5 x 4 Answers) Each of these is worth 0.5 points. However, showing the calculation is must. If calculation is missing, the whole answer won't get any credit.arrow_forward
- Binomial Prob. Question: A new teaching method claims to improve student engagement. A survey reveals that 60% of students find this method engaging. If 15 students are randomly selected, what is the probability that: a) Exactly 9 students find the method engaging?b) At least 7 students find the method engaging? (2 points = 1 x 2 answers) Provide answers in the yellow cellsarrow_forwardIn a survey of 2273 adults, 739 say they believe in UFOS. Construct a 95% confidence interval for the population proportion of adults who believe in UFOs. A 95% confidence interval for the population proportion is ( ☐, ☐ ). (Round to three decimal places as needed.)arrow_forwardFind the minimum sample size n needed to estimate μ for the given values of c, σ, and E. C=0.98, σ 6.7, and E = 2 Assume that a preliminary sample has at least 30 members. n = (Round up to the nearest whole number.)arrow_forward
- In a survey of 2193 adults in a recent year, 1233 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. The 90% confidence interval for the population proportion p is (Round to three decimal places as needed.) J.D) .arrow_forwardLet p be the population proportion for the following condition. Find the point estimates for p and q. In a survey of 1143 adults from country A, 317 said that they were not confident that the food they eat in country A is safe. The point estimate for p, p, is (Round to three decimal places as needed.) ...arrow_forward(c) Because logistic regression predicts probabilities of outcomes, observations used to build a logistic regression model need not be independent. A. false: all observations must be independent B. true C. false: only observations with the same outcome need to be independent I ANSWERED: A. false: all observations must be independent. (This was marked wrong but I have no idea why. Isn't this a basic assumption of logistic regression)arrow_forward
- Business discussarrow_forwardSpam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output: Estimate SE Z Pr(>|Z|) (Intercept) -0.8161 0.086 -9.4895 0 to_multiple -2.5651 0.3052 -8.4047 0 winner 1.5801 0.3156 5.0067 0 format -0.1528 0.1136 -1.3451 0.1786 re_subj -2.8401 0.363 -7.824 0 (a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…arrow_forwardConsider an event X comprised of three outcomes whose probabilities are 9/18, 1/18,and 6/18. Compute the probability of the complement of the event. Question content area bottom Part 1 A.1/2 B.2/18 C.16/18 D.16/3arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL


