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| m102705 | The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged 19-64 and persons aged 65 and over.
a. Obtain a relative-frequency distribution of health status for persons aged 19-64 and a relative-frequency distribution of health status for persons aged 65 and over.
b. Draw a pie chart for both age groups.
c. Compare your pie charts. |
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| m102706 | The National Center for Health Statistics compiles data on injuries and publishes the information in Vital and Health Statistics. A contingency table for injuries in the United States, by circumstance and gender, is as follows. Frequencies are in millions.
a. Find P(C1).
b. Find P(C1 | S2).
c. Are events C1 and S2 independent? Explain your answer.
d. Is the event that an injured person is male independent of the event that an injured person was hurt at home? Explain your answer. |
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| m102707 | The National Center for Health Statistics compiles information on activity limitations. Results are published in Vital and Health Statistics. The data show that 13.6% of males and 14.4% of females have an activity limitation. Are gender and activity limitation statistically independent? Explain your answer. |
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| m102708 | The National Center for Health Statistics publishes information about visits to the dentist in National Health Interview Survey. Here is a joint probability distribution for the length of time (in years) since last visit to a dentist or other dental health professional, by age, for U.S. adults during one year.
For a U.S. adult selected at random, determine the following probabilities and interpret your results in terms of percentages.
a. P(T1)
b. P(not A2)
c. P(A4 & T5)
d. P(T4 | A1)
e. P(A1 | T4) |
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| m102709 | The National Education Association collects data on teacher salaries and publishes results in Estimates of School Statistics Database. Independent samples of 100 secondary school teachers and 125 elementary school teachers yielded the data, in thousands of dollars, on annual salaries as presented on the Weiss Stats site.
a. Obtain histograms, box-plots, and normal probability plots of the two samples.
b. Based on your results from part (a), given the choice between using a pooled t-test or a Mann-Whitney test, which would you choose? Explain your answer.
c. Use both the pooled t-test and the Mann-Whitney test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the average salary of secondary school teachers exceeds that of elementary school teachers. Compare the results of the two tests. |
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| m102710 | The National Fire Protection Association reported that house fires in the United States result in $6.8 billion in losses annually (National Fire Protection Association, September 2015). Suppose a random sample of 50 house fires in San Antonio yields a mean loss of $18,503. If the population standard deviation is s 5 $3300, what is the margin of error for a 95% confidence interval? What would you recommend if the study required a margin of error of $300 or less? |
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| m102711 | The National Governors Association publishes data on U.S. governors in Governors Political Affiliations & Terms of Office. Based on that document, we obtained the following frequency distribution for U.S. governors, as of 2013.
Party ______________ Frequency
Democratic ................... 20
Republican ................... 30
Two U.S. governors are selected at random without replacement.
a. Find the probability that the first is a Republican and the second a Democrat.
b. Find the probability that both are Republicans.
c. Draw a tree diagram for this problem similar to the one shown in Fig. 4.25 on page 194.
d. What is the probability that the two governors selected have the same political-party affiliation?
e. What is the probability that the two governors selected have different political-party affiliations? |
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| m102712 | The National Institute on Drug Abuse issued the report monitoring the Future, which addressed the issue of drinking, cigarette, and smokeless tobacco use for eighth, tenth, and twelfth graders. During one year, 12,900 twelfth graders were asked the question, "How frequently have you smoked cigarettes during the past 30 days?" Based on their responses, we constructed the following percentage distribution for all twelfth graders.
Find the probability that, within the last 30 days, a randomly selected twelfth grader
a. Smoked.
b. Smoked at least one cigarette per day.
c. Smoked between 6 and 34 cigarettes per day, inclusive. |
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| m102713 | The number of hospital beds available in community hospitals is decreasing. Through advancement in care and technology, hospitals are getting more efficient. However, the aging and increasingly obese and diabetic population intensifies the need. The American Hospital Association Annual Survey, published by the American Hospital Association (AHA), gave the number of hospital beds available per 1000 people for each of the 50 states plus the District of Columbia for 2010. Following is a stem-and-leaf diagram of the data. The stems represent units and the leaves tenths (e.g., the first entry is 1.7).
How many states (including the District of Columbia) had
a. At least three but less than four hospital beds per 1000 people available?
b. At least four and a half hospital beds per 1000 people available? |
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| m102714 | The objective of the article, "Caffeinated and Caffeine-free Beverages and Risk of Type 2 Diabetes" (American Journal of Clinical Nutrition, Vol. 97, No. 1, pp. 155-166) by S. Bhupathiraju et al., was to examine the association between caffeinated beverages and type 2 diabetes risk. The mean and standard deviation of the body mass index (BMI) for a sample of 10,215 women who drink at least one caffeinated carbonated beverage a day are 25.7 and 5.3, respectively.
a. At least how many women in the sample have a BMI of between 15.1 and 36.3?
b. Fill in the blanks: At least 89% of the women in the sample have BMIs between ______and ______. |
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| m102715 | The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.
(i) Ogive
(ii) Ogive Showing Cumulative Percentage of Data
(a) How were the percentage shown in graph (ii) computed?
(b) How many states have average per capita income less than 37.5 thousand dollars?
(c) How many states have average per capita income between 42.5 and 52.5 thousand dollars?
(d) What percentage of the states have average per capita income more than 47.5 thousand dollars? |
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| m102716 | The Old Course at St. Andrews in Scotland is home of the British Open, one of the major tournaments in professional golf. The Hole O Cross Out, known by both European and American professional golfers as one of the friendliest holes at St. Andrews, is the fifth hole, a 514-yard, par 5 hole with an open fairway and a large green. As one reporter put it, "If players think before they drive, they will easily walk away with birdies and pars." The scores on the Hole O Cross Out posted by a sample of 156 golf professionals are presented on the Weiss-Stats site. Use those data and the technology of your choice to decide whether, on average, professional golfers score better than par on the Hole O Cross Out.
Perform the required hypothesis test at the 0.01 level of significance.
(a). Employ the Wilcoxon signed-rank test.
(b). Employ the t-test.
(c). Compare your results from parts (a) and (b). |
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| m102717 | The owners of a motel in Florida have noticed that in the long run, about 40% of the people who stop and inquire about a room for the night actually rent a room.
(a) Quota Problem How many inquiries must the owner answer to be 99% sure of renting at least one room?
(b) If 25 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals? |
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| m102718 | The paired sign test can be used whether or not the paired difference variable has a symmetric distribution.
a. If the distribution is in fact symmetric, the paired Wilcoxon signed-rank test is preferable. Why do you think that is so?
b. What advantage does the paired sign test have over the paired Wilcoxon signed-rank test? |
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| m102719 | The Peace Corps is an independent U.S. government agency that provides trained volunteers for countries requesting assistance. According to Peacecorps.org, as of September 2012, volunteers currently serve in about 76 different host countries. The average age of a volunteer is about 28 years old. The following table reports the percentage of total volunteers serving by geographic region.
Region __________________ Percent of volunteers
Africa ........................................... 43%
Latin America .................................. 21%
Eastern Europe/Central Asia ................. 15%
Asia .............................................. 10%
Caribbean ....................................... 4%
North Africa/Middle East .................... 4%
Pacific Islands .................................. 3%
a. Use the table to design a procedure for obtaining a stratified sample (with proportional allocation) of 50 Peace Corps volunteers.
b. If stratified random sampling with proportional allocation is used to select the sample of 50 Peace Corps volunteers, how many would be selected from the Caribbean? |
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| m102720 | The percentage of Texans not covered by health care insurance in 2015 was 17% (The Henry J. Kaiser Family Foundation website, December 5, 2015). The Texas Health and Human Services Commission (HHSC) has been charged with conducting a sample survey to obtain more current information.
a. What sample size would you recommend if the HHSC s goal is to estimate the current proportion of Texans without health care insurance with a margin of error of .03? Use a 95% confidence level.
b. Repeat part (a) using a 99% confidence level. |
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| m102721 | The personnel of fice at a large electronics fi rm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a fi rst interview is normally distributed, with mean ( = 35 minutes and standard deviation ( = 7 minutes.
(a) What is the probability that a fi rst interview will last 40 minutes or longer?
(b) Nine fi rst interviews are usually scheduled per day. What is the probability that the average length of time for the nine interviews will be 40 minutes or longer? |
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| m102722 | The Pew Internet & American Life Project compiles data on smartphone ownership and publishes the results in the document Smartphone Ownership. The first two columns of the following table provide a percentage distribution for age of U.S. adults. The third column of the table shows the percentage of people in each age group who own a smartphone.
Suppose that a U.S. adult is selected at random. Determine the probability that the person selected
a. Owns a smartphone, given that he or she is between 18 and 24 years old.
b. Owns a smartphone
c. Is between 18 and 24 years old, given that he or she owns a smartphone.
d. Interpret your answers in parts (a)-(c) in terms of percentages. |
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| m102723 | The Pew Research Center conducted a survey of 45,535 adults in 40 countries to learn about major concerns for the future (Pew Research Center website, December 5, 2015). The survey results showed that 20,901 of the respondents are very concerned about climate change.
a. What is the point estimate of the population proportion of adults who are very concerned about climate change?
b. At 90% confidence, what is the margin of error?
c. Develop a 90% confidence interval for the population proportion of adults who are very concerned about climate change.
d. Develop a 95% confidence interval for the population proportion of adults who are very concerned about climate change. |
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| m102724 | The PGA TOUR provides various statistics on performance of players in the Professional Golfers Association of America. For the week ending September 9, 2013, the year-to-date leader for longest average drive was Bubba Watson. For his 773 drives, he averaged 298.5 yards. Assume a standard deviation of 19.7 yards.
The quantitative data set under consideration has roughly a bell-shaped distribution. For each exercise,
a. Construct a graph similar to Fig. 3.8 on page 118.
b. Apply Property 1 of the empirical rule to make pertinent statements about the observations in the sample.
c. Repeat part (b) for Property 2 of the empirical rule.
d. Repeat part (b) for Property 3 of the empirical rule. |
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