Cumulative Exam — Cumulative exam Answers

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3

Which of the following displays is a relative frequency bar graph?

A
A bar graph titled eye color has color on the x-axis. Blue, 8; brown, 10; green, 6; hazel, 5; gray, 1.
Option A
B
A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
Option B
C
A bar graph titled Caffeinated Drinks has drink on the x-axis. Coffee, 9; tea, 8; soda, 8; energy, 3.
Option C
D
A bar graph titled social media preferences has platform on the x-axis . Upstart, 4; Aster, 18; Babble, 15; Techy, 12.
Option D
4

A trade school would like to measure the long-term success of their graduates after they leave the school. The school emails a survey requesting information from graduates about their work experience. One question asks graduates to share their annual salary, and the results of the question will be shared in a brochure for incoming students. Is it likely that the survey results will provide an accurate estimate of mean annual salary for all of the school’s graduates?

A
The survey will provide a reasonable estimate of mean annual salary because all graduates were sent the email survey.
B
The survey will likely overestimate mean annual salary because those with higher salaries may be more likely to respond to the survey.
C
The survey will likely underestimate mean annual salary because there may be more graduates with lower salaries than higher salaries.
D
The survey will likely overestimate the mean annual salary because the email was only sent to graduates with jobs in their chosen field.
5

People of different ages were asked the question "Do you listen to audiobooks?” The bar graph below displays the percentage of "yes” responses for different age groups.

Question illustration
A
No, because the bars are all the same width.
B
No, because the scale starts at 0.
C
Yes, because the bars are not the same height.
D
Yes, because the scale does not start at 0.
9

A nutritionist would like to estimate the number of times adults exercise each week. To collect information, the nutritionist emails the members of the local fitness center. Which of the following describes the bias that may arise from the results?

A
This is a convenience sample and likely overestimates the frequency of exercise.
B
This is a convenience sample and likely underestimates the frequency of exercise.
C
This is a voluntary response sample and likely overestimates the frequency of exercise.
D
This is a voluntary response sample and likely underestimates the frequency of exercise.
12

Brand A and brand B of frozen green beans both list a weight of 32 ounces on their bags. Because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. An inspector takes a random sample of 25 bags of green beans of each type and records their weights. The weights and their relative frequencies are summarized in the histograms.

Question illustration
A
The median weight for both types is between 32.1 and 32.2 ounces.
B
The median weight for both types is between 32.0 and 32.1 ounces.
C
The median weight for brand B is less than the median weight of brand A.
D
The median weight for brand B is greater than the median weight of brand A.
13

A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

Question illustration
A
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective than B.
B
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that B is more effective than A.
C
No, because a difference in mean rating of 1.5 or less occurred 167 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
D
No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
14

A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0).

Question illustration
A
One-fourth
Option A
B
One-half
Option B
C
StartFraction 1 Over 8 EndFraction
Option C
D
StartFraction 1 Over 16 EndFraction
Option D
17

In a statistics class, students were asked how many siblings they have. The mean number of siblings for the class is 3.08 with a standard deviation of 1.61 siblings. The z-score for a student with four siblings is 0.57. Which of the following statements is the best interpretation of the z-score?

A
The number of siblings for this student is in the 57th percentile.
B
This student has 0.57 fewer siblings than the mean number of siblings.
C
The number of siblings for this student is 0.57 standard deviations above the mean number of siblings.
D
The number of siblings for this student is 0.57 standard deviations below the mean number of siblings.
18

Kaitlyn and Allison took a standardized algebra test in different states. Kaitlyn takes the test for Virginia and scores a 458. Allison takes the test for North Carolina and scores a 185. Suppose the mean and standard deviation for the algebra scores for Virginia are 405 and 30, respectively, and the mean and standard deviation for the algebra scores for North Carolina are 152 and 20, respectively. Which student did better on her algebra test?

A
Kaitlyn and Allison did equally well since their scores are both above the mean.
B
Kaitlyn did better since her z-score is higher than Allison’s z-score.
C
Allison did better since her z-score is higher than Kaitlyn’s z-score.
D
Allison did better since her z-score is closer to the mean than Kaitlyn’s z-score.
19

The parallel dotplots below display the number of absences for students in each of two classes.

Question illustration
A
The range for the distribution of the number of absences is larger for class D.
B
The range for the distribution of the number of absences is larger for class C.
C
The IQR for the distribution of the number of absences is larger for class D.
D
The IQR for the distribution of the number of absences is larger for class C.
20

A therapist wants to study the effects of yoga and meditation on stress relief. She has 60 volunteers who experience varying levels of stress. Half of the participants will be assigned to practice yoga for one month and the other half will practice meditation. Before the experiment begins, all of the participants will be asked to rate their stress levels on a scale from 0 to 10, with 0 representing "no stress” and 10 representing "highest level of stress.” At the end of one month, the participants will be asked to rate their stress levels again. The differences in stress levels will be compared.

A
The volunteers’ names are all placed on equal-sized slips of paper and these slips are put into a hat. The therapist draws 30 slips of paper and the corresponding volunteers are placed into the yoga group. The remaining 30 volunteers are placed in the meditation group. After one month, the stress levels between the two groups are measured and compared.
B
Volunteers are put together in groups of two based on stress level. For each group of two, a coin is flipped. If it lands on heads, then the first person is placed in the yoga group and if it is tails, then the first person is placed in the meditation group. The other person will be placed in the other group. After one month, the stress levels between the two participants are measured and compared.
C
The volunteers’ names are all placed on equal-sized slips of paper, and these slips are put into a hat. After the hat is shaken, a slip of paper is drawn and the corresponding volunteer is placed in the yoga group. This is repeated until the yoga group has 30 volunteers. The remaining 30 volunteers are placed in the meditation group. After one month, the stress levels between the two groups are measured and compared.
D
The volunteers are grouped based on their current stress levels. The 30 volunteers with the highest levels of reported stress are placed in one group and the remaining 30 volunteers are placed in another group. The therapist flips a coin. If it lands on heads, then the group with the highest stress levels will receive the yoga treatment. If it lands on tails, then this group will receive the meditation treatment. After one month, the stress levels will be compared between the two groups.

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