Question 1

A realtor wants to compare the variability of sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, andD) Four properties are randomly selected from each neighborhood and the ratios recorded for each were collected. Which of the following tests will be the most appropriate?

Accepted Answer

Levene's test is used to assess the equality of variances for a variable calculated for two or more groups, making it appropriate for comparing the variability of sales-to-appraisal ratios across the four neighborhoods.

Question 2

Are Japanese managers more motivated than American managers? A randomly selected group of 100 managers from each group were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The average and standard deviation of the SSATL scores are computed. The standard deviations of the SSATL scores suggest that the standard deviation from the two groups is very different. Which of the following tests will be the most appropriate?

Accepted Answer

Since the standard deviations of the SSATL scores for the two groups are very different, a separate-variance t test would be the most appropriate choice. A pooled-variance t test assumes equal variances in the two groups, which is not the case here. The Z test for proportion is not applicable as this study does not involve proportions. The t test for mean would be appropriate if the standard deviations were similar, but since they are not, a separate-variance t test is the better option.

Question 3

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) Which of the following tests will be the most appropriate?

Accepted Answer

The Tukey-Kramer multiple comparisons procedure for one-way ANOVA is appropriate here because it is used to compare the means of more than two groups (in this case, four software packages) to determine if there are any statistically significant differences between them.

Question 4

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. Which of the following tests will be the most appropriate?

Accepted Answer

The appropriate test in this scenario is the Z test for proportion because we are comparing a proportion (the number of households with VCRs) to a specified value (5,000 out of 20,000 households). The sample size of 300 is large enough for the Central Limit Theorem to apply, allowing us to use the normal distribution and calculate a z-score to make the comparison. The other tests listed (t tests) are appropriate for comparing means, not proportions.

Question 5

Every spring semester, the School of Business coordinates with local business leaders a luncheon for graduating seniors, their families, and friends. Corporate sponsorship pays for the lunches of each of the seniors, but students have to purchase tickets to cover the cost of lunches served to guests they bring with them. Data on the number of guests each graduating senior invited to the luncheon and the number of graduating seniors in each category were collected. A histogram can be used to present this information.

Accepted Answer

A histogram is a useful tool to present the distribution of numerical data, including the number of guests invited by each graduating senior and the number of graduating seniors in each category. It can display the frequency or proportion of guests in each group or category, making it easy to interpret and compare the data.

Question 6

The opinions (classified as "for," "neutral" or "against") of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball. You can present this information using a scatter plot.

Accepted Answer

A scatter plot is not a suitable way to represent categorical data such as opinions classified as "for," "neutral," or "against." A bar chart or a pie chart might be more appropriate in this case.

Question 7

A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Data were collected on the class status ("freshman," "sophomore," "junior" or "senior") of 50 students enrolled in one of his economics course. A side-by-side bar chart can be used to present this information.

Accepted Answer

The answer of A professor of economics at a small...

Question 8

A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). Which of the following distributions would you use to figure out the probability that all of them will fail?

Accepted Answer

The binomial distribution is used when there are a fixed number of independent trials, each with only two possible outcomes (success or failure), and the probability of success is constant across all trials. In this case, we have three independent trials (the opening of three businesses), each with a probability of success of 0.6 and a probability of failure of 0.4. Therefore, we can use the binomial distribution to calculate the probability that all three businesses will fail.

Question 9

A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). An ogive can be used to present this information.

Accepted Answer

An ogive can be used to display cumulative frequency data, such as the distribution of ratings for television programming quality.

Question 10

A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Data on the percentage of men and women depicting preference for Pepsi were collected. Which of the following tests will you use to find out if there is any difference in preference between the different gender groups?

Accepted Answer

The Z test for difference in proportions is the appropriate test to use in this situation as we are comparing the proportions of preference for Pepsi between two groups (men and women) and the data is categorical. The paired t test is used when we have paired data, while the chi-square test for variance is used when we are comparing variances. The Wilcoxon rank sum test is used when the data is ordinal or non-normally distributed.

Question 11

Suppose that past history shows that 60% of college students prefer coca-cola. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer coca-cola?

Accepted Answer

The question involves a probability distribution for a categorical variable (preference for coca-cola). The binomial distribution is used for a fixed number of independent trials with two possible outcomes (success or failure), which is the case when selecting a sample of 10 students who either prefer or do not prefer coca-cola. Therefore, the binomial distribution is the best choice for this question.

Question 12

Suppose the probability of a car accident taking place anywhere on a stretch of a 20- mile highway is the same. Which of the following distributions would you use to figure out the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

Accepted Answer

The uniform distribution is used when all outcomes have an equal probability of occurring. In this case, the probability of a car accident occurring at any point on the 20-mile highway is the same, and so we can use the uniform distribution to calculate the probability of an accident occurring between the 5-mile and 15-mile posts. The other distributions listed are not appropriate for this scenario.

Question 13

You have 5 stocks in your investment portfolio. You want to keep track of your portfolio's performance over the last 2 years. You have data on each of the stock's average price and the number of shares of each stock for every day of the last 2 years. Which of the following would be the most appropriate analysis to perform?

Accepted Answer

The Laspeyres price index is used to measure the performance of a portfolio over time by comparing the total value of the portfolio at different points in time, using a fixed base period for weights.

Question 14

The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 1.. Suppose that the probability of a chocolate chip parts in a cookie is constant across cookies and the number of chocolate chip parts in one cookie is independent of the number in any other cookie. Which of the following distributions would you use to figure out the probability that any particular cookie being inspected has 4.0 chip parts?

Accepted Answer

The answer of The quality control manager of Marilyn's Cookies...

Question 15

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 5 such alarms in your home and they operate independently. Which of the following distributions would you use to figure out the probability that all of them will function properly in case of a fire?

Accepted Answer

The scenario described fits the criteria for a binomial distribution, where we have a fixed number of independent trials (5 smoke alarms), each with two possible outcomes (function properly or not), and a constant probability of success (0.8). The binomial distribution is used to calculate the probability of a certain number of successes (in this case, all 5 alarms) occurring in a fixed number of trials.

Question 16

The amount of juice that can be squeezed from a randomly selected orange out a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?

Accepted Answer

The amount of juice that can be squeezed from a randomly selected orange is a continuous variable that is likely to follow a normal distribution. This is because the sizes of oranges in the box are approximately the same, so the amount of juice that can be squeezed will not vary drastically. The central limit theorem also suggests that the sample means from a large number of oranges will be normally distributed.

Question 17

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. Which of the following distributions would you use to figure out the probability that out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios?

Accepted Answer

The hypergeometric distribution is used when we want to draw a sample without replacement from a finite population that contains both successes and failures. In this case, we have 48 new cars, 12 of which have defective radios. Therefore, the population contains both "successes" (defective cars) and "failures" (non-defective cars). The question asks for the probability that, out of a sample of 8 cars, no more than 2 have defective radios. This is a classic hypergeometric distribution problem, where we are drawing a sample without replacement from a finite population. Therefore, the correct distribution to use is the hypergeometric distribution.

Question 18

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Which of the following tests will be the most appropriate to find out if there is any difference in crop yield among the 3 varieties?

Accepted Answer

The answer of An agronomist wants to compare the crop...

Question 19

An insurance company evaluates many variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of 100 insured drivers and recorded, X, the amount of claims each made in the last 3 years. A Pareto chart can be used to present this information.

Accepted Answer

The answer of An insurance company evaluates many variables about...

Question 20

At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. A stem-and-leaf display can be used to present this information.

Accepted Answer

A stem-and-leaf display is a useful tool for organizing and presenting numerical data, particularly when dealing with a smaller range of values like the number of employees overseen by information systems officers in this scenario.

Quiz 19: Statistical Analysis Scenarios and Distributions

The opinions (classified as "for," "neutral" or "against") of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball. You can present this information using a scatter plot.

A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). An ogive can be used to present this information.

Suppose that past history shows that 60% of college students prefer coca-cola. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer coca-cola?

Suppose the probability of a car accident taking place anywhere on a stretch of a 20- mile highway is the same. Which of the following distributions would you use to figure out the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

The amount of juice that can be squeezed from a randomly selected orange out a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?