Practice Test 1

Applicants to California community colleges are asked to indicate one of these education goals at the time of​ application: transfer to a​ four-year institution, an AA​ degree, a CTE​ certificate, job​ retraining, or personal enrichment. In a group of 500​ applications, describe a bar graph of these data that would have the least amount of variability. Also describe a bar graph that would have the most variability.

A bar graph with the least variability would be one where most of the applicants had the same education​ goal, for example to transfer. A bar graph with the most variability would be one in which the applicants were equally divided among the five choices.

The histograms show the monthly costs for operating two makes of​ cars: Ford and BMW. Which make typically has higher monthly​ costs? Which make has more variation in​ costs?

A. Ford, center, higher, BMW. B.Ford, spead, higher, BMW.

The accompanying histogram shows the number of runs scored by baseball teams for three seasons. The distribution is roughly unimodal and​ symmetric, with a mean of 687 and a standard deviation of 68 runs. An interval one standard deviation above and below the mean is marked on the histogram. Assume the values in a bin are distributed uniformly. For​ example, if the leftmost line is at the​ midpoint, then half of that​ bin's values are below the line and half are above. Complete parts​ (a) through​ (c) below.

A.68 B. ​68% of the data falls in the interval from619 to 755The estimate is very close to the value predicted by the Empirical Rule.

The following histograms show the number of years in office for Democratic and Republican U.S. senators. Complete parts​ (a) through​ (d) below.

A.Both distributions are​ right-skewed. B.The medians should be used because the mean should not be used when the data are skewed. C.The interquartile ranges should be used because the standard deviation should not be used when the data are skewed. D.Longer than Similar

The accompanying dotplots show the number of calories in a sample of cereals from two​ manufacturers, K and G. a. Compare the center and the spread for each dotplot. b. Based on this​ sample, cereals from which manufacturer tend to have more variation in​ calories?

A.Both manufacturers have a similar​ center, but the spread for manufacturer K is greater than the spread for manufacturer G B. Cereals from manufacturer K tend to have more variation in calories because the spread of manufacturer K is greater than the spread of manufacturer G.

A survey records the heights of a representative sample of youths aged 14 to 20. The accompanying histograms show data for the heights of males and females. If you were comparing the heights of males and​ females, which measures of center and spread would you​ use? Why?

A.Mean and standard deviation B.The distributions are roughly symmetric and unimodal.

The boxplot displayed shows the average ticket price for four professional sports leagues. Complete parts​ (a) and​ (b) below.

A.Sport C,Sport, D. B.less expensive than,a lower median than,Sport B,higher IQR. high-priced,high-priced

Name two measures of the center of a​ distribution, and state the conditions under which each is preferred for describing the typical value of a single data set.

A.mean, the distribution is relatively symmetric. B.median,the distribution is strongly skewed.b

The top seven movies based on DC comic book characters for the U.S. box office as of fall 2017 are shown in the accompanying​ table, rounded to the nearest million. Complete parts​ (a) through​ (c) below.

B. The middle​ 50% of the top 7 DC movies had domestic grosses that varied by as much as this value. C.The IQR depends on many observations and is therefore more reliable.

What are Pareto​ charts?

Bar charts that are sorted from most frequent to least frequent

A group of educators want to determine how effective tutoring is in raising​ students' grades in a math​ class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring​ worked? If​ not, explain why not and suggest a confounding variable.

Because this was an observational​ study, it only shows an​ association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades.

Distributions of gestation periods​ (lengths of​ pregnancy) for a particular animal are roughly​ bell-shaped. The mean gestation period for this animal is 282 ​days, and the standard deviation is 10 days for females who go into spontaneous labor. Which is more​ unusual, a baby being born 20 days early or a baby being born 20 days​ late? Explain.

Both events are equally likely

Distributions of gestation periods​ (lengths of​ pregnancy) for a particular animal are roughly​ bell-shaped. The mean gestation period for this animal is 267 ​days, and the standard deviation is 15 days for females who go into spontaneous labor. Which is more​ unusual, a baby being born 30 days early or a baby being born 30 days​ late? Explain.

Both events are equally likely.

The accompanying dotplots show the number of calories in a sample of cereals from two​ manufacturers, K and G. a. Compare the center and the spread for each dotplot. b. Based on this​ sample, cereals from which manufacturer tend to have more variation in​ calories?

Both manufacturers have a similar​ center, but the spread for manufacturer G is greater than the spread for manufacturer K. Cereals from manufacturer G tend to have more variation in calories because the spread of manufacturer G is greater than the spread of manufacturer K.

The accompanying table gives the percent of market controlled by the most popular Internet browsers in one year. Sketch an appropriate graph of the​ distribution, and comment on its important features.

Pie chart,Pareto chart. Browser 1 controls the highest market share.

When you are comparing two sets of​ data, and one set is strongly skewed and the other is​ symmetric, which measures of the center and variation should you choose for the​ comparison?

The medians and interquartile ranges

Cartilage is a​ smooth, rubber-like padding that protects the long bones in the body at the joints. A study by Lu et. al. in Arthritis Care​ & Research found that women who drank one glass of milk daily had​ 32% thicker, healthier cartilage than women who did not. Researchers obtained information on milk consumption through questionnaires and measured cartilage through​ x-rays. In the​ article, research​ concluded, "Our study suggested that frequent milk intake may be associated with reduced OA progression in​ women." Does this study show drinking milk causes increased cartilage​ production? Why or why​ not?

The study is an observational​ study, because there is no mention of random assignment.​ No, we cannot conclude causation when there is not random assignment.

The data were collected from a statistics class. The column heads give the​ variable, and each of the rows represents a student in the class. There are observations on how many​ people?

There are observations on 4 people

Indicate whether the study is an observational study or a controlled experiment. Patients with multiple sclerosis are randomly assigned a new drug or placebo and are then given a test of coordination after six months.

This is a controlled experiment because the patients were assigned drugs by those conducting the study.

Indicate whether the following study is an observational study or a controlled experiment. A researcher is interested in the effect of music on memory. She randomly divides a group of students into three​ groups: those who will listen to quiet​ music, those who will listen to loud​ music, and those who will not listen to music. After the appropriate music is played​ (or not​ played), she gives all the students a memory test.

This is a controlled experiment. She assigns students to the control and treatment groups at random in order to control for all relevant factors aside from the effect of music on​ memory, which is essential to conducting a controlled experiment.

In 2017 a pollution index was calculated for a sample of cities in the eastern states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was 40.6 points with a standard deviation of 11.4 points. Complete parts​ (a) through​ (c) below.

a.95 b.68 c.​No, because 50.3 falls within two standard deviations away from the​ mean, and it is therefore not an unusually high pollution index.

The data were collected from a statistics class. The column heads give the​ variable, and each of the rows represents a student in the class. Give an example of another categorical variable that might have been recorded for these students.

first name

The data were collected from a statistics class. The column heads give the​ variable, and each of the rows represents a student in the class. Give an example of another categorical variable that might have been recorded for these students.

home town

In a​ boxplot, the vertical line inside the box marks the location of the​ _______.

median.

The histograms show the Body Mass Index for 90 females and 89 males. Compare the distributions of BMIs for women and men. Be sure to compare the​ shapes, the​ centers, and the amount of variation for the two groups.

right-skewed,unimodal,right-skewed,bimodal. b. The centers appear​ similar, but the peak for men occurs at a higher BMI. c.The​ women's values are more spread out.

The data in the accompanying table were collected from a statistics class. The first row gives the​ variable, and each of the other rows represents a student in the class. Suppose you wanted to know whether ring size and height were associated. Could you do that with this data​ table? If​ so, which variables would you​ use?

​Yes, this data table could be used. Ring Size and Height would be used.

The data in the accompanying table were collected from a statistics class. The first row gives the​ variable, and each of the other rows represents a student in the class. Suppose you wanted to know whether living situation was associated with number of units the student had acquired. Could you do that with this data​ table? If​ so, which variables would you​ use?

​Yes, this data table could be used. Variables College Units Acquired and Living Situation would be used.