Cumulative AP Practice Test 1 Solutions - Page 276

Q: How do the solutions compare machine A and machine B using distribution properties?

They compare center, spread, and shape: machine A has a lower median than machine B, a substantially smaller range, and a symmetric shape, while machine B is skewed left. Overall, machine B tends to have higher cardiovascular fitness values.

Q: Why might the company prefer machine B versus machine A for advertising?

Machine B is preferred for advertising the highest overall gain because its median and mean are higher. Machine A is preferred for advertising consistent gains because it shows less variation, with a smaller IQR and smaller standard deviation.

Q: What conclusions are drawn from the regression of weekly sales on shelf length?

The solutions state a linear model is reasonable due to a strong positive linear association. They provide the regression equation and prediction for x = 5 feet, report the residual standard deviation, explain that R^2 = 0.982 indicates most variation is explained, and caution against interpreting the intercept due to extrapolation beyond the data range.

Sep 30, 2026

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Cumulative AP Practice Test 1 solutions for Page 276 provide detailed answers for multiple items, labeled AP1.1 through AP1.17. The solutions interpret statistical comparisons of cardiovascular fitness measures between machine A and machine B, evaluating center, spread, shape, symmetry, skewness, median and mean differences, and consistency via IQR and standard deviation. Additional sections address study design and sampling methods for retail sales incentives, and interpret linear regression for weekly sales versus shelf length, including equations, residual standard deviation, and the meaning of R^2 and the intercept.

LanguageEnglish

CategoryExam

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Pages2

Reading Time5 min

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AP1.15

Compare cardiovascular fitness distributions

Choose machines based on median/consistency

Discuss limitations and sampling approach

AP1.16

Random assignment using random numbers

Matched pairs design

AP1.17

Linear model justification

Regression equation and predictions

Residual standard deviation and R^2

Interpretation of the intercept

Cumulative AP Practice Test 1 Solutions Page 276 AP1 .1 d. AP1 .2 e. AP 1.3 b. AP 1.4 c. AP 1.5 a. AP 1.6 c. AP 1.7 e. AP 1.8 e. AP 1.9 d. AP 1.10 d. AP 1.11 d. AP 1.12 b. AP1 .13 b. AP1 .14 a. AP1.15 (a) When comparing data sets it is expected that center, spread, and shape will be addressed. The median for the distribution of cardiovascular fitness measures for machine A (28) is lower than the median of the distribution of cardiovascular fitness measures for machine B (38) . The range for the distribution of cardiovascular fitness measures for machine A is substantially smaller than the range of the distribution of cardiovascular fitness measures for machine B (32 < 57). (Alternatively, the IQR for machine A (37 – 22 = 15) is lower than the IQR for machine B (47 – 25 = 22).) The distribution of cardiovascular fitness measures for machine A is reasonably symmetric in shape, while the distribution of cardiovascular fitness measures for machine B is skewed to the left (toward the lower values) . In general, the cardiovascular fitness measures for machine B tend to be higher than those for machine A. (b) The company should choose machine B if they want to advertise it as achieving the highest overall gain in cardiovascular fitness. The median for machine B is higher than it is for machine A, as is the mean ( xB = 35.4 versus xA = 28.9 ). (c) The company should choose machine A if they want to advertise it as achieving the most consistent gains in cardiovascular fitness. Machine A exhibits less variation in gains than does machine B. The IQR for machine A is 15, while the IQR for machine B is 22. Additionally, the standard deviation for machine A is 9.38, while the standard deviation for machine B is 16.19. (d) Volunteers were used for the experiment and these volunteers may be different in some way from the general population of those who are interested in cardiovascular fitness. Another reason is that the experiment was conducted at only one fitness center. Results may vary at other fitness centers in this city and in other cities. If the company had taken a random sample of all people who were interested in cardiovascular fitness it could infer to this much larger population. If the company had randomly selected a number of fitness centers from across the country and then randomly selected members of each fitness center to participate in the experiment, the company would be using a stratified random sampling method with the fitness centers serving as the strata. AP1.16 (a) Assign each retail sales district a number from 1-60 using a random number generator. Order the sales districts numerically. The first 30 are assigned to the monetary incentives group and the remaining 30 to the intangibles incentive group. After a specified period of time compare the mean sales for each of the treatment groups to see if there is a difference. (b) Assign each retail sales district a number between 01 and 60. Go through the random number table taking two digits at a time. The first 30 two-digit numbers between 01 and 60 to come up are assigned to the monetary incentives group. Thereminder will be assigned to the intangible incentives group. 07511 88915 41267 16853 84569 79367 32337 03316 The districts labeled 07, 51, and 18 are the first three to be assigned to the monetary incentives group.(c) It would be better to use a matched pairs design. There could be a large variation among the sales figures for the various districts due to the various sizes of those districts across the different regions of the United States. Matching the districts based on their size reduces the effect of variation among the experimental units due to their size on the response variable—sales volume. Pair the two largest districts in size, the next two largest, down to the two smallest districts. For each pair, pick one of the districts and flip a coin if the flip is “heads” this district is assigned to the monetary incenti

FAQs

How do the solutions compare machine A and machine B using distribution properties?

They compare center, spread, and shape: machine A has a lower median than machine B, a substantially smaller range, and a symmetric shape, while machine B is skewed left. Overall, machine B tends to have higher cardiovascular fitness values.

Why might the company prefer machine B versus machine A for advertising?

Machine B is preferred for advertising the highest overall gain because its median and mean are higher. Machine A is preferred for advertising consistent gains because it shows less variation, with a smaller IQR and smaller standard deviation.

What conclusions are drawn from the regression of weekly sales on shelf length?

The solutions state a linear model is reasonable due to a strong positive linear association. They provide the regression equation and prediction for x = 5 feet, report the residual standard deviation, explain that R^2 = 0.982 indicates most variation is explained, and caution against interpreting the intercept due to extrapolation beyond the data range.

Sep 30, 2026

Uploaded by A glass of water