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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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| m102725 | The physical fitness score for a population of police officers at a local police station is 72, with a standard deviation of 7 on a 100-point physical endurance scale. Suppose the police chief selects a sample of 49 local police officers from this population and records a mean physical fitness rating on this scale equal to 74. He conducts a one-sample z test to determine whether physical endurance increased at a .05 level of significance.
(a) State the value of the test statistic and whether to retain or reject the null hypothesis.
(b) Compute effect size using Cohen s d. |
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| m102726 | The Poisson distribution (Section 5.4) gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1/ βe-x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities.
If a and b are any numbers such that 0 6 a 6 b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is
P(a < x < b) = e - a/β - e -b/β
Notice that by de finition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are
( = β and ( = β
The number e = 2.71828 . . . is used throughout probability, statistics and mathematics. The key ex is conveniently located on most calculators.
The Poisson and exponential distributions have a special relationship. Specifi cally, it can be shown that the waiting time between successive Poisson arrivals (i.e., successes or rare events) has an exponential distribution with β = 1/(, where l is the average number of Poisson successes (rare events) per unit of time. For more on this topic, please see Problem 20.
Fatal accidents on scheduled domestic passenger flights are rare events. I |
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| m102727 | The probability is 0.314 that the gestation period of a woman will exceed 9 months. In 4000 human gestation periods, roughly how many will exceed 9 months? |
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| m102728 | The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money? |
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| m102729 | The probability that a single radar station will detect an enemy plane is 0.65.
(a) Quota Problem How many such stations are required for 98% certainty that an enemy plane flying over will be detected by at least one station?
(b) If four stations are in use, what is the expected number of stations that will detect an enemy plane? |
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