1. The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below.
Based on the histogram, which of the following statements must be true?
(A) The minimum price is $250,000.
(B) The maximum price is $2,500,000.
(C) The median price is not greater than $750,000.
(D) The mean price is between $500,000 and $750,000.
(E) The upper quartile of the prices is greater than $1,500,000.
2. As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medical records of 1,436 people. The table below summarizes tanning booth use for people in the study who did and did not have skin cancer.
Of the people in the study who had skin cancer, what fraction used a tanning booth?
3. A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher?
(A)H0: p=0.5 and Ha : P>0.5
(B)H0: p=0.5 and Ha : P≠0.5
(C)H0: p=0.5 and Ha : P＜0.5
(D)H0: p＞0.5 and Ha : P≠0.5
(E)H0: p＞0.5 and Ha : P=0.5
4. A company determines the mean and standard deviation of the number of sick days taken by its employees in one year. Which of the following is the best description of the standard deviation?
(A) Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees
(B) Approximately the median distance between the number of sick days taken by individual employees and the median number of sick days taken by all employees
(C) The distance between the greatest number of sick days taken by an employee and the mean number of sick days taken by all employees
(D) The number of days separating the fewest sick days taken and the most sick days taken when considering all employees
(E) The number of days separating the fewest sick days taken and the most sick days taken when considering the middle 50 percent of the distribution
1. Natural gas is used in some households to heat the home, to heat the water, and to cook. A utility company sent the following bar chart to a household to show the amount of natural gas, measured in therms (a unit of heat energy), that the household used last year. The chart shows the number of therms and the average monthly temperature, in degrees Fahrenheit, for each month of the year.
(a) Describe how the number of therms used each month changed over the year.
(b) Construct an appropriate graph that shows the relationship between the number of therms used and the average monthly temperature.
(c) Describe what your graph in part (b) reveals about the relationship between the number of therms used and the average monthly temperature that is not revealed on the bar chart sent by the utility company.
2. Swedish researchers investigated the relationship between chocolate consumption and stroke. The researchers gave a questionnaire about eating habits to a randomly selected sample of Swedish men. Based on the responses to the questionnaire, the men were classified into two groups. Group A consisted of the 9,250 men who ate the most chocolate per week, and group B consisted of the 9,250 men who ate the least chocolate per week. The researchers tracked the men’s health for ten years. During that time, there were 458 cases of stroke among the men in group A and 543 cases of stroke among the men in group B.
(a) Do the data provide convincing statistical evidence that Swedish men who would be classified into group A have a lower probability of stroke than Swedish men who would be classified into group B?
If you need more room for your work in part (a), use the space below.
(b) A report in a newspaper concluded that Swedish men can reduce their probability of stroke by eating more chocolate. Based on the description of the investigation, was the conclusion appropriate? Justify your answer.
3. A large retail company has 500 stores in the United States and 300 stores in Europe. The average number of employees per store is 200, for a total of 100,000 employees in the United States and 60,000 employees in Europe. The company is considering offering employees one of two new benefits—one additional day of paid vacation per year or a small increase in pay. A survey will be given to a sample of employees to investigate which benefit is preferred and whether there is a difference in preference between employees in the United States and employees in Europe.
Two sampling methods have been proposed.
Sampling method 1: The company will randomly select 8 stores from its 800 stores. All employees at the 8 selected stores will be asked which benefit they prefer.
Sampling method 2: The company will randomly select 1,000 employees from a list of all employees at the United States stores and 600 employees from a list of all employees at the European stores. All 1,600 selected employees will be asked which benefit they prefer.
(a) One of the two methods results in a stratified sample of employees and the other results in a cluster sample of employees.
(i) Identify the sampling method that results in a stratified sample of employees, and identify the strata.
Sampling method number:
(ii) Identify the sampling method that results in a cluster sample of employees, and identify the clusters.
Sampling method number:
(b) Give one statistical advantage and one statistical disadvantage of using sampling method 1.
(c) Explain a statistical advantage of using sampling method 2 rather than using a simple random sample.