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mathematics
statistics

Questions and Answers of Statistics

The head of institutional research at a university believed that the mean age of full-time students was declining. In 1995, the mean age of a full-time student was known to be 27.4 years. After
Explain the difference between statistical signiﬁcance and practical significance.
The life expectancy of a male during the course of the past 100 years is approximately 27,725 days. Go to Wikipedia.com and download the data that represent the lifespan of chief justices of Canada
A simple random sample of size n = 19 is drawn from a population that is normally distributed. The sample mean is found to be 0.8, and the sample standard deviation is found to be 0.4. Test whether
A simple random sample of size n = 200 individuals with a valid driver’s license is asked if they drive an American-made automobile. Of the 200 individuals surveyed, 115 responded that they drive
A simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be 23.8, and the sample standard deviation is found to be 6.3. Is the
A simple random sample of size n = 65 is drawn from a population. The sample mean is found to be 583.1, and the sample standard deviation is found to be 114.9. Is the population mean different from
A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be 108.5, and the sample standard deviation is found to be 17.9. Is the population mean greater than 100
A simple random sample of size n = 320 adults was asked their favorite ice cream ﬂavor. Of the 320 individuals surveyed, 58 responded that they preferred mint chocolate chip. Do less than 25% of
Does playing Mozart for unborn babies result in children with higher IQs? A psychologist obtains a random sample of 20 mothers in the ﬁrst trimester of their pregnancy. The mothers are asked to
In October 1945, the Gallup organization asked 1487 randomly sampled Americans, “Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them
In 2001, 23% of American university undergraduate students had at least one tattoo. A health practitioner suspects that the percent has changed since then. She obtains a random sample of 1026
Among individuals who have credit cards in 2010, the mean number of cards is 3.5 according to the Federal Reserve Bank of Boston. Treat the individuals who have credit cards in the Sullivan
The manufacturer of a toner cartridge claims the mean number of printouts is 10,000 for each cartridge. A consumer advocate is concerned that the actual mean number of printouts is lower. He selects
A certain vehicle emission inspection station advertises that the wait time for customers is less than 8 minutes. A local resident is skeptical and collects a random sample of 49 wait times for
With a previous contractor, the mean time to replace a streetlight was 3.2 days. A city councilwoman thinks that the new contractor is not getting the streetlights replaced as quickly. She selects a
According to the research ï¬rm Toluna, the proportion of individuals who text while driving is 0.26. Suppose a random sample of 60 individuals are asked to disclose if they text while driving.
Politicians often form their positions on various policies through polling. Suppose the U.S. Congress is considering passage of a tax increase to pay down the national debt. National polls suggest
Suppose the mean wait-time for a telephone reservation agent at a large airline is 43 seconds. A manager with the airline is concerned that business may be lost due to customers having to wait too
The Gallup organization conducted a survey and asked, “What do you think is the ideal number of children for a family to have?” The results of the survey are shown in the table.Ideal Number of
Assume that the paired differences come from a population that is normally distributed.(a) Compute di = Xi - Yi for each pair of data.(b) Compute d and sd.(c) Test the hypothesis that md 6 0 at the a
Assume that the populations are normally distributed and that independent sampling occurred.(a) Test the hypothesis that µ1 ‰ µ2 at the Î± = 0.1 level ofsigniï¬cance for the given
Test the hypothesis that µ1 > µ2 at the Î± = 0.01 level of signiï¬cance for the given sample data.Assume that the populations are normally distributed and that
A random sample of n1 = 555 individuals results in x1 = 451 successes. An independent sample of n2 = 600 individuals results in x2 = 510 successes. Does this represent sufﬁcient evidence to
A statistics student heard that an individual€™s arm span is equal to the individual€™s height. To test this hypothesis, the student used a random sample of 10 students and obtained the
A student wanted to determine whether the wait time in the drive-through at McDonald€™s differed from that at Wendy€™s. She used a random sample of 30 cars at McDonald€™s and 27 cars at
Osteoporosis is a condition in which people experience decreased bone mass and an increase in the risk of bone fracture. Actonel is a drug that helps combat osteoporosis in postmenopausal women. In
In the General Social Survey, individuals were asked whether civic duty included voting and whether it included serving on a jury. The results of the survey are shown in the table. Is there a
A nutritionist wants to estimate the difference between the percentage of men and women who have high cholesterol. What sample size should be obtained if she wishes the estimate to be within 2
Construct and interpret a 95% conï¬dence interval for the population mean difference between height and arm span using the data from Problem 7. What does the interval lead us to conclude
Construct and interpret a 95% conï¬dence interval about µM - µW using the data from Problem 8. How might a marketing executive with McDonald€™s use this information?
(a) Compute di = Xi - Yi for each pair of data.(b) Compute d-bar and sd.(c) Test the hypothesis that µd ‰ 0 at the Î± = 0.01 level of signiï¬cance.(d) Compute a 95% conï¬dence
Assume that the populations are normally distributed and that independent sampling occurred.(a) Test the hypothesis that µ1 ‰ µ2 at the Î± = 0.1 level ofsigniï¬cance for the given
Test the hypothesis that µ1Assume that the populations are normally distributed and that independent sampling occurred.
A random sample of n1 = 650 individuals results in x1 = 156 successes. An independent sample of n2 = 550 individuals results in x2 = 143 successes. Does this represent sufﬁcient evidence to
A researcher wants to know whether the acidity of rain (pH) near Houston, Texas, is signiï¬cantly different from that near Chicago, Illinois. He randomly selects 12 rain dates in Texas and 14
In a study conducted to determine the role that sleep disorders play in academic performance, researcher Jane Gaultney conducted a survey of 1845 college students. The students completed a survey to
In Problem 9 from Section 11.2 we analyzed data in which an SUV crashed into the rear bumper of a car. Now we are going to reverse roles and allow the car traveling 10 miles per hour to collide into
Zoloft is a drug used to treat obsessive-compulsive disorder (OCD). In randomized, double-blind clinical trials, 926 patients diagnosed with OCD were randomly divided into two groups.Subjects in
Does hypnotism result in a different success rate for men and women who are trying to quit smoking? Researchers at Science magazine analyzed studies involving 5600 male and female smokers. Of the
The General Social Survey asked the following two questions of randomly selected individuals.€¢ Do you favor or oppose the death penalty for persons convicted of murder?€¢ Should it be possible
A researcher wants to estimate the difference between the percentage of individuals without a high school diploma who smoke and the percentage of individuals with bachelor’s degrees who smoke. What
It is commonplace to gain weight after quitting smoking. Does the drug Naltrexone help limit weight gain when individuals quit smoking? To determine the effectiveness of this drug, 147 subjects who
An educator wants to determine whether a new curriculum signiﬁcantly improves standardized test scores for third grade students. She randomly divides 80 third-graders into two groups. Group 1 is
Conduct each test at the α = 0.05 level of signiﬁcance by determining (a) The null and alternative hypotheses, (b) The test statistic, (c) The critical value, and (d) The P-value. Assume that
Conduct each test at the α = 0.05 level of signiﬁcance by determining (a) The null and alternative hypotheses, (b) The test statistic, (c) The critical value, and (d) The P-value. Assume that
Conduct each test at the α = 0.05 level of signiﬁcance by determining (a) The null and alternative hypotheses, (b) The test statistic, (c) The critical value, and (d) The P-value. Assume that
Conduct each test at the α = 0.05 level of signiﬁcance by determining (a) The null and alternative hypotheses, (b) The test statistic, (c) The critical value, and (d) The P-value. Assume that
Construct a conﬁdence interval for p1 - p2 at the given level of conﬁdence.x1 = 368, n1 = 541, x2 = 421, n2 = 593, 90% conﬁdence
Construct a conﬁdence interval for p1 - p2 at the given level of conﬁdence.x1 = 109, n1 = 475, x2 = 78, n2 = 325, 99% conﬁdence
Construct a conﬁdence interval for p1 - p2 at the given level of conﬁdence.x1 = 28, n1 = 254, x2 = 36, n2 = 301, 95% conﬁdence.
Construct a conﬁdence interval for p1 - p2 at the given level of conﬁdence.x1 = 804, n1 = 874, x2 = 892, n2 = 954, 95% conﬁdence.
Test whether the population proportions differ at the Î± = 0.05 level of signiï¬cance by determining(a) The null and alternative hypotheses,(b) The test statistic,(c) The
Test whether the population proportions differ at the Î± = 0.05 level of signiï¬cance by determining(a) The null and alternative hypotheses,(b) The test statistic,(c) The
The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis. It is typically administered to infants starting around 2 months of age. In randomized, double-blind clinical
The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis. It is typically administered to infants starting around 2 months of age. In randomized, double-blind clinical
In October 1947, the Gallup organization surveyed 1100 adult Americans and asked, “Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?” Of the 1100 adults
The Pew Research Group conducted a poll in which they asked, “Are you in favor of, or opposed to, executing persons as a general policy when the crime was committed while under the age of 18?” Of
The Harris Poll conducted a survey in which they asked, “How many tattoos do you currently have on your body?” Of the 1205 males surveyed, 181 responded that they had at least one tattoo. Of the
The body mass index (BMI) of an individual is one measure that is used to judge whether an individual is overweight or not. A BMI between 20 and 25 indicates that one is at a normal weight. In a
In clinical trials of the allergy medicine Clarinex (5 mg), it was reported that 50 out of 1655 individuals in the Clarinex group and 31 out of 1652 individuals in the placebo group experienced dry
In clinical trials for treatment of a skin disorder, 642 of 2105 patients receiving the current standard treatment were cured of the disorder and 697 of 2115 patients receiving a new proposed
In March 2003, the Pew Research Group surveyed 1508 adult Americans and asked, “Do you believe the United States made the right or wrong decision to use military force in Iraq?” Of the 1508 adult
In many colleges and universities around the country, educators are changing their approach to instruction from a “teacher/lecture-centered model” to a “student-centered model” where students
In the Sullivan Statistics Survey, respondents were asked, “Would you be willing to pay higher taxes if the tax revenue went directly toward deﬁcit reduction?” Treat the respondents as a simple
In the Sullivan Statistics Survey, respondents were asked to disclose whether they have a Facebook account. Treat the respondents as a simple random sample of adult Americans.(a) What proportion of
Teenie Matlock and Caitlin Fausey asked students to read two sentences about hypothetical politicians. Ninety-eight students read, “Last year, Mark was having an affair with his assistant and was
Suppose John has an online company that sells custom rims for cars. John has designed two different Web pages that he wants to use to sell his rims online. However, he cannot decide which page to go
In a survey of 3029 adult Americans, the Harris Poll asked people whether they smoked cigarettes and whether they always wear a seat belt in a car. The table shows the results of the survey. For each
The Gallup organization conducted a survey in which they asked 1020 adult Americans whether they felt low-income people paid their fair share of taxes. Then they asked whether they felt high-income
Have you ever been frustrated by computer telephone systems that do not understand your voice commands? Quite a bit of effort goes into designing these systems to minimize voice-recognition errors.
Look at the data in Table comparing the effectiveness of two ointments on. Conduct the appropriate test to determine if one ointment has a different effectiveness than the other. Use the Î± = 0.05
In October 2010, the Gallup organization surveyed 1134 American adults and found that 441 had a gun in the home. In October 2009, the Gallup organization had surveyed 1134 American adults and found
Accupril, a medication supplied by Pï¬zer Pharmaceuticals, is meant to control hypertension. In clinical trials of Accupril, 2142 subjects were divided into two groups. The 1563
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular, sustained physical activity. What sample size should be obtained if she wishes
An educator wants to determine the difference between the proportion of males and females who have completed 4 or more years of college. What sample size should be obtained if she wishes the estimate
On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided in two groups. The
Assume that the differences are normally distributed.(a) Determine di = Xi - Yi for each pair of data.(b) Compute d-bar and sd.(c) Test if µd (d) Compute a 95% conï¬dence interval about the
Assume that the differences are normally distributed.(a) Determine di = Xi - Yi for each pair of data.(b) Compute d and sd.(c) Test if µd ‰ 0 at the Î± = 0.01 level of signiï¬cance.(d)
Yale University graduate student J. Kiley Hamlin conducted an experiment in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby
Since its removal from the banned substances list in 2004 by the World Anti-Doping Agency, caffeine has been used by athletes with the expectancy that it enhances their workout and performance. Many
The following data represent the muzzle velocity (in feet per second) of rounds ï¬red from a 155-mm gun. For each round, two measurements of the velocity were recorded using two different
In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key on seeing a blue screen.
It is a commonly held belief that SUVs are safer than cars. If an SUV and car are in a collision, does the SUV sustain less damage (as suggested by the cost of repair)? The Insurance Institute for
A Secchi disk is an 8-inch-diameter weighted disk that is painted black and white and attached to a rope. The disk is lowered into water and the depth (in inches) at which it is no longer visible is
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both he father and son in inches and obtains
A quality-control manager at an amusement park feels that the amount of time that people spend waiting in line for the American Eagle roller coaster is too long. To determine if a new
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that
The following data represent the daily rental for a compact automobile charged by two car rental companies, Thrifty and Hertz, in 10 locations. Test whether Thrifty is less expensive than Hertz at
To illustrate the effects of driving under the inï¬‚uence (DUI) of alcohol, a police ofï¬cer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured
An automotive researcher wanted to estimate the difference in distance required to come to a complete stop while traveling 40 miles per hour on wet versus dry pavement. Because car type plays a role,
Octane is a measure of how much the fuel can be compressed before it spontaneously ignites. Some people believe that higher-octane fuels result in better gas mileage for their cars. To test this
You are a passenger in a single-propeller-driven aircraft that experiences engine failure in the middle of a ï¬‚ight. The pilot wants to maximize the distance that the plane can glide to increase
(a) Test whether µ1 ‰ µ2 at the Î± = 0.05 level of signiï¬cance for the given sample data.(b) Construct a 95% conï¬dence interval about µ1 - µ2.Assume that the populations are
Assume that the populations are normally distributed.(a) Test whether µ1 ‰ µ2 at the a = 0.05 level of signiï¬cance for the given sample data.(b) Construct a 95% conï¬dence interval
Assume that the populations are normally distributed.(a) Test whether µ1 > µ2 at the Î± = 0.1 level of signiï¬cance for the given sample data.(b) Construct a 90% conï¬dence interval
Assume that the populations are normally distributed.(a) Test whether µ1 (b) Construct a 95% conï¬dence interval about µ1 - µ2.
Test whether µ1Assume that the populations are normally distributed.
Test whether µ1 > µ2 at the Î± = 0.05 level of signiï¬cance for the given sample data.Assume that the populations are normally distributed.
Clifford Adelman, a researcher with the Department of Education, followed a cohort of students who graduated from high school in 1992. He monitored the progress the students made toward completing a

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