Exam 1: Exploring and Understanding Data

To determine if people's preference in dogs had changed in the recent years, organizers of a local dog show asked people who attended the show to indicate which breed was their favorite. This information was compiled by dog breed and gender of the people who responded. The table summarizes the responses. -Which of the W's are unknown for these data?

In June 2003 Consumer Reports published an article on some sport-utility vehicles they had tested recently. They reported some basic information about each of the vehicles and the results of some tests conducted by their staff. Among other things, the article told the brand of each vehicle, its price, and whether it had a standard or automatic transmission. They reported the vehicle's fuel economy, its acceleration (number of seconds to go from zero to 60 mph), and its braking distance to stop from 60 mph. The article also rated each vehicle's reliability as much better than average, better than average, average, worse, or much worse than average. -Describe the W's, if the information is given: • Who: • What: • When: • Where: • How: • Why:

Which of these variables is most likely to follow a Normal model for U.S. adults?

Students taking an intro stats class reported the number of credit hours that they were taking that quarter. Summary statistics are shown in the table. 16.65 s 2.96 min 5 Q1 15 median 16 Q3 19 max 28 a. Suppose that the college charges $73 per credit hour plus a flat student fee of $35 per quarter. For example, a student taking 12 credit hours would pay $ $\$ 35 + \$ 73 ( 12 ) = \$ 911 \text { for }$ that quarter. i. What is the mean fee paid? ii. What is the standard deviation for the fees paid? iii. What is the median fee paid? iv. What is the IQR for the fees paid? b. Twenty-eight credit hours seems like a lot. Would you consider 28 credit hours to be unusually high? Explain.

Which of these variables is most likely to follow a Normal model?

Book sales A publishing company pays its sales staff $\$ 600$ a week plus a commission of $\$ 0.50$ per book sold. For example, a salesman who sold 440 books earned $600 + 0.50 ( 440 ) =$ $\$ 820$ . a. The table shows summary statistics for the number of books the large sales staff sold last week. Fill in the table to show the statistics for the pay these people earned. Statistic Books Sold \ Earned Mean 640 St. dev. 360 IQR 450 Maximum 1420 b. The newest employee had a pretty good week. Among all the salespeople her pay corresponded to a $z$ -score of $+ 1.80$ . What was the $z$ -score of the number of books she sold?

A research company frequently monitors trends in the use of social media by American Adults. The results of one survey of 1846 randomly selected adults looked at social media use versus age group. The table summarizes the survey results. -Write a sentence or two about the conditional relative frequency distribution of ages of social media users.

We collect these data from 50 male students. Which variable is categorical?

Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is some variation in that. The actual weights are pretty well represented by a normal model with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this model.

One of the reasons that the Monitoring the Future (MTF) project was started was "to study changes in the beliefs, attitudes, and behavior of young people in the United States." Data are collected from 8th, 10th, and 12th graders each year. To get a representative nationwide sample, surveys are given to a randomly selected group of students. In Spring 2004, students were asked about alcohol, illegal drug, and cigarette use. Describe the W's, if the information is given. If the information is not given, state that it is not specified. • Who: • What: • When: • Where: • How: • Why:

A professor has kept records on grades that students have earned in his class. If he wants to Examine the percentage of students earning the grades A, B, C, D, and F during the most recent Term, which kind of plot could he make?

At www.census.gov you can create a "population pyramid" for any country. These pyramids are back-to-back histograms. This pyramid shows Mexico's 2000 female population and the census bureau's projection for 2050. Write a few sentences summarizing the changes that are forecast.

Suppose that a Normal model describes fuel economy (miles per gallon) for automobiles and that a Saturn has a standardized score (z $( \mathrm { z } - \mathrm { score } ) \text { of } + 2.2$ This means that Saturns . . .

The average scores for Wisconsin schools on the ACT are summarized in the ogive shown. Estimate The IQR of the average scores.

Soda cans A machine that fills cans with soda fills according to a Normal model with mean 12.1 ounces and standard deviation 0.05 ounces. a. If the cans claim to have 12 ounces of soda each, what percent of cans are under-filled? b. Management wants to ensure that only 1% of cans are under-filled. i. Scenario 1: If the mean fill of the cans remains at 12.1 ounces, what standard deviation does the filling machine need to have to achieve this goal? ii. Scenario 2: If the standard deviation is to remain at 0.05 ounces, what mean does the filling machine need to have to achieve this goal?

In order to plan transportation and parking needs at a private high school, administrators asked students how they get to school. Some rode a school bus, some rode in with parents or friends, and others used "personal" transportation skateboards, or just walked. The table summarizes the responses from boys and girls. -Do you think mode of transportation is independent of gender? Give statistical evidence to support your conclusion.

A research company frequently monitors trends in the use of social media by American Adults. The results of one survey of 1846 randomly selected adults looked at social media use versus age group. The table summarizes the survey results. -Which of the W's are unknown for these data?

How do sports salaries compare? Two sets of histograms below show the distributions of salaries for Major League Baseball and the National Football League. Give two reasons why the second set of histograms makes it easier to compare the distributions. Then write a few sentences comparing the salary distributions for the two sports.

Concrete thickness A roadway construction process uses a machine that pours concrete onto the roadway and measures the thickness of the concrete so the roadway will measure up to the required depth in inches. The concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if the roadway is thinner than the minimum 23 inch thickness, the company sets the machine to average 26 inches for the batches of concrete. They believe the thickness level of the machine's concrete output can be described by a Normal model with standard deviation 1.75 inches. [Show work] a. What percent of the concrete roadway is under the minimum depth? b. The company's lawyers insist that no more than 3% of the output be under the limit. Because of the expense of operating the machine, they cannot afford to reset the mean to a higher value. Instead they will try to reduce the standard deviation to achieve the "only 3% under" goal. What standard deviation must they attain? c. Explain what achieving a smaller standard deviation means in this context.

Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (Shanthy A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239): -Find the following: a. What percent of the young girls reported that they drink milk? b. What percent of the young girls were in the 1989-1991 survey? c. What percent of the young girls who reported that they drink milk were in the 1989-1991 survey? d. What percent of the young girls in 1989-1991 reported they drink milk?