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statistics the art and science

Questions and Answers of Statistics The Art and Science

The pH of a liquid is a measure of its acidity or alkalinity. Pure water has a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are basic
The dataset BaseballHits gives 2010 season statistics for all Major League Baseball teams. We treat this as a sample of all MLB teams in all years. Computer output of descriptive statistics for the
We are interested in whether or not the average cost of a house in Canton, NY (the hometown of the Lock family) is significantly different from the national average of $265,000. Table 6.5 and the
The dataset HomesFor- Sale has data on houses available for sale in three Mid-Atlantic states (NY, NJ, and PA). Table 6.4 (also used in Exercise 6.100) shows the mean and standard deviation from the
Susan is in charge of quality control at a small fruit juice bottling plant. Each bottle produced is supposed to contain exactly 12 fluid ounces (fl oz) of juice. Susan decides to test this by
In the mid-1990s a Nabisco marketing campaign claimed that there were at least 1000 chips in every bag of Chips Ahoy! cookies. A group of Air Force cadets collected a sample of 42 bags of Chips Ahoy!
It is generally recommended that adults sleep at least 8 hours each night. One of the authors recently asked some of her students (undergraduate and graduate students at Harvard) how many hours each
In a study conducted in Paris, France, equal amounts of pigeon feed were spread on the ground in two adjacent locations. A human feeder was present in both sites, with one acting as a hostile feeder
Autistic children often have a small head circumference at birth, followed by a sudden and excessive increase in head circumference during the first year of life. A recent study examined the brain
Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. It is nearly impossible for most people to reliably list all the people
Test H0: μ = 500 vs Ha: μ ≠ 500 using the sample results x̅ = 432, s = 118, with n = 75.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a5%significance
Test H0: μ = 4 vs Ha: μ ≠ 4 using the sample results x̅ = 4.8, s = 2.3, with n = 15.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a5%significance
Test H0: μ = 10 vs Ha: μ > 10 using the sample results x̅ = 13.2, s = 8.7, with n = 12.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5%
Test H0: μ = 120 vs Ha: μ < 120 using the sample results x̅ = 112.3, s = 18.4, with n = 100.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5%
Test H0: μ = 100 vs Ha : μ < 100 using the sample results x̅ = 91.7, s = 12.5, with n = 30.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5%
Test H0: μ = 15 vs Ha : μ > 15 using the sample results x̅ = 17.2, s = 6.4, with n = 40.Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5%
Use technology and the NutritionStudy dataset to find a 95% confidence interval for the mean number of grams of fiber (Fiber) people eat in a day. Interpret the answer in context.
Use technology and the RestaurantTips dataset to find a 95% confidence interval for the mean tip percentage (PctTip) at the restaurant. Interpret the answer in context.
Find the sample size needed to give, with 95% confidence, a margin of error within ±3, if the estimated standard deviation is σ̃ = 100. If the estimated standard deviation is σ̃ = 50. If the
Find the sample size needed to give a margin of error within ±3 with 99% confidence. With 95% confidence. With 90% confidence. Assume that we use σ̃ = 30 as our estimate of the standard deviation
Find the sample size needed to give, with 95% confidence, a margin of error within ±10. Within ±5. Within ±1. Assume that we use σ̃ = 30 as our estimate of the standard deviation in each case.
In Exercise 6.128, we see that plastic microparticles are contaminating the world’s shorelines and that much of the pollution appears to come from fibers from washing polyester clothes. The same
Plastic microparticles are contaminating the world’s shorelines (see Exercise 6.129), and much of this pollution appears to come from fibers from washing polyester clothes. The worst offender
In Exercise 6.116 on page 386, we see that the average number of close confidants in a random sample of 2006 US adults is 2.2 with a standard deviation of 1.4. If we want to estimate the number of
Using the dataset NutritionStudy, we calculate that the average number of grams of fat consumed in a day for the sample of n = 315 US adults in the study is x̅ = 77.03 grams with s = 33.83 grams.(a)
In the 2010-11 National Hockey League (NHL) regular season, the number of penalty minutes per game for each of the 30 teams ranged from a low of 8.8 for the Florida Panthers to a high of 18.0 for the
Mean price of a used Mustang car online, in $1000s, using data in MustangPrice with x̅ = 15.98, s = 11.11, and n = 25Find a 95% confidence interval for the mean two ways: using StatKey or other
Mean distance of a commute for a worker in Atlanta, using data in CommuteAtlanta with x̅ = 18.156 miles, s = 13.798, and n = 500Find a 95% confidence interval for the mean two ways: using StatKey or
The dataset BaseballHits gives 2010 season statistics for all Major League Baseball (MLB) teams. We treat this as a sample of all MLB teams in all years. Computer output of descriptive statistics for
The dataset RestaurantTips has information from First Crush bistro in northern New York state. Computer output of descriptive statistics for the variable giving the size of the tip is shown:(a) How
Data A.1 on page 136 introduces a study in which mice that had a light on at night (rather than complete darkness) ate most of their calories when they should have been resting. These mice gained a
Data A.1 on page 136 introduces a study in which mice that had a dim light on at night (rather than complete darkness) ate most of their calories when they should have been resting. These mice gained
Scientists estimate that there are 10 times more bacterial cells in your body than your own body’s cells, and new studies on bacteria in the gut indicate that your gut microbes might be influencing
Gribbles are small, pale white, marine worms that bore through wood. While sometimes considered a pest since they can wreck wooden docks and piers, they are now being studied to determine whether the
In a recent study, 2006 randomly selected US adults (age 18 or older) were asked to give the number of people in the last six months ‘‘with whom you discussed matters that are important to
In the dataset StudentSurvey, 361 students recorded the number of hours of television they watched per week. The average is x̅ = 6.504 hours with a standard deviation of 5.584. Find a 99% confidence
A margin of error within ±12 with 95% confidence, assuming we estimate that σ ≈ 125What sample size is needed to give the desired margin of error in estimating a population mean with the
A margin of error within ±0.5 with 90% confidence, if we make a reasonable estimate that σ = 25What sample size is needed to give the desired margin of error in estimating a population mean with
A margin of error within ±1 with 99% confidence, assuming a sample from a similar population had s = 3.4What sample size is needed to give the desired margin of error in estimating a population mean
A margin of error within ±5 with 95% confidence, assuming a previous sample had s = 18What sample size is needed to give the desired margin of error in estimating a population mean with the
A 99% confidence interval for μ using the sample results x̅ = 88.3, s = 32.1, and n = 15Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give
A 99% confidence interval for μ using the sample results x̅ = 46.1, s = 12.5, and n = 10Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give
A 90% confidence interval for μ using the sample results x̅ = 137.0, s = 53.9, and n = 50Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give
A 90% confidence interval for μ using the sample results x̅ = 3.1, s = 0.4, and n = 100Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the
A 95% confidence interval for μ using the sample results x̅ = 84.6, s = 7.8, and n = 42Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the
A 95% confidence interval for μ using the sample results x̅ = 12.7, s = 5.6, and n = 30Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results.
The AllCountries dataset includes land area, in square kilometers, for all 213 countries in the world. The mean land area for all the countries is 608,120 sq km with standard deviation 1,766,860. For
Exercise 6.89 describes scores on the Critical Reading portion of the Scholastic Aptitude Test (SAT) for college-bound students in the class of 2010. Critical Reading scores are approximately
Most IQ tests scale the scores so that the mean IQ score is μ = 100 and standard deviation is σ = 15. Suppose that 30 fourth graders in one class are given such an IQ test that is appropriate for
Answer the same questions using Figure 6.10 as in Exercise 6.100 except assume that each histogram represents only 15 homes. Is the t-distribution appropriate to model sample means of housing price
The dataset HomesForSale has data on price in thousands of dollars for houses for sale in three Mid-Atlantic states (NY, NJ, and PA). Figure 6.10 shows a histogram for a random sample of the asking
Mean body temperature, in ◦F, using the data in BodyTemp50 with n = 50, x̅ = 98.26, and s = 0.765Use StatKey or other technology to generate a bootstrap distribution of sample means and find the
Mean price of used Mustang cars online (in $1000s) using the data in MustangPrice with n = 25, x̅ = 15.98, and s = 11.11Use StatKey or other technology to generate a bootstrap distribution of sample
Mean commute time in Atlanta, in minutes, using the data in CommuteAtlanta with n = 500, x̅ = 29.11, and s = 20.72Use StatKey or other technology to generate a bootstrap distribution of sample means
Mean number of penalty minutes for NHL players using the data in Ottawa Senators with n = 24, x̅ = 49.58, and s = 49.14Use StatKey or other technology to generate a bootstrap distribution of sample
Asample with n = 10, xÌ… = 508.5, and s = 21.5We give summary statistics and a dotplot for a sample. In each case, indicate whether or not it is appropriate to use the t-distribution. If
A sample with n = 18, xÌ… = 87.9, and s = 10.6We give summary statistics and a dotplot for a sample. In each case, indicate whether or not it is appropriate to use the t-distribution. If
A sample with n = 75, xÌ… = 18.92, and s = 10.1We give summary statistics and a dotplot for a sample. In each case, indicate whether or not it is appropriate to use the t-distribution. If
A sample with n = 12, xÌ… = 7.6, and s = 1.6We give summary statistics and a dotplot for a sample. In each case, indicate whether or not it is appropriate to use the t-distribution. If it
Compute the standard error for sample means from populations all with mean μ = 100 and with standard deviations σ = 5, σ = 25, and σ = 75 using a sample size of n = 100. Discuss the effect of the
Compute the standard error for sample means from a population with mean μ = 100 and standard deviation σ = 25 for sample sizes of n = 30, n = 200, and n = 1000. What effect does increasing the
The Critical Reading portion of the Scholastic Aptitude Test (SAT) was taken by 1,547,990 college bound students in the class of 2010. Scores on that portion of the test range from 200 to 800 and the
For the class of 2010, the average score on the Writing portion of the SAT (Scholastic Aptitude Test) is 492 with a standard deviation of 111. Find the mean and standard deviation of the distribution
For the class of 2010, the average score on the Mathematics portion of the SAT (Scholastic Aptitude Test) is 516 with a standard deviation of 116. Find the mean and standard deviation of the
The All Countries dataset includes land area, in square kilometers, for all 213 countries in the world. The median land area for all the countries is 94,080 sq km and the mean is 608,120 sq km with
Choose one of the following datasets: USStates, StudentSurvey, AllCountries, or NBAPlayers2011, and then select any two quantitative variables that we have not yet analyzed. Use technology to create
Sample proportions of sample size n = 100 from a population with p = 0.4Find the mean and standard error of the sample proportions two ways:(a) Use StatKey or other technology to simulate at least
Proportion of home team wins in soccer, using p̂ = 0.583 with n = 120Find a 95% confidence interval for the proportion two ways, using StatKey or other technology and percentiles from a bootstrap
Proportion of Reese’s Pieces that are orange, using p̂ = 0.48 with n = 150Find a 95% confidence interval for the proportion two ways, using StatKey or other technology and percentiles from a
Find the sample size needed to give, with 95% confidence, a margin of error within±6%when estimating a proportion. Within ±4%. Within ±1%. (Assume no prior knowledge about the population
Find the sample size needed to give a margin of error to estimate a proportion within ±3% with 99% confidence. With 95% confidence. With 90% confidence. (Assume no prior knowledge about the
Find the sample size needed to give, with 95% confidence, a margin of error within ±3% when estimating a proportion. First, find the sample size needed if we have no prior knowledge about the
A survey of 1000 adults in the US conducted in March 2011 asked ‘‘Do you favor or oppose ‘sin taxes’ on soda and junk food?” The proportion in favor of taxing these foods was 32%.(a) Find a
A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±2% with 95% confidence, and we do not have any
An advertising firm plans to have a sample of individuals view a commercial on a ‘‘sunscreen pill” that one can swallow to provide mild SPF protection throughout the day. After viewing the
In April 2012, the Gallup Poll reported that in a random sample of 1016 US adults, only 17% approve of the way Congress is handling its job.(a) Use the poll results to estimate the proportion of all
One of the variables in the dataset CommuteAtlanta, introduced in Data 3.3 on page 193, gives the sex of each commuter in the sample. Use technology and the dataset to construct and interpret a 95%
The dataset ICU-Admissions, introduced in Data 2.3 on page 66, includes information on 200 patients admitted to an Intensive Care Unit. One of the variables, Status, indicates whether each patient
As of 2011, Division I college football in the US does not have a tournament-style playoff to pick a national champion. In a random survey conducted by Quinnipiac University, people who identified
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Approximately 10% of Americans are left-handed (we will treat this as a known population parameter). A study on the relationship between handedness and profession found that in a random sample of 105
A telephone survey of 1000 randomly selected US adults found that 31% of them say they believe in ghosts. Does this provide evidence that more than 1 in 4 US adults believe in ghosts? Clearly show
There were 2430 Major League Baseball (MLB) games played in 2009, and the home team won the game in 54.9% of the games. If we consider the games played in 2009 as a sample of all MLB games, test to
The percent of US adults who know their neighbors appears to be trending up. A survey of 2255 randomly selected US adults conducted in November 2010 found that 51% said they know all or most of their
Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that
In Example 2.6 on page 51 we consider a survey of students who were asked to choose an award they would like to win from among an Academy Award, Nobel Prize, and Olympic gold medal. If the awards are
In Data 4.1 on page 220 we consider an experiment to see if dogs tend to resemble their owners. In the study, 16 of 25 dogs were correctly matched with the owner when two choices were provided. To
In Exercise 4.40 on page 236, we introduce a series of Euchre games played between two teams: Team A and Team B. After 40 games, Team A has won 16 times and Team B has won 24 times. Can we conclude
The data in Nutrition- Study, introduced in Exercise 1.13 on page 13, include information on nutrition and health habits of a sample of 315 people. One of the variables is Smoke, indicating whether a
The data in NutritionStudy, introduced in Exercise 1.13 on page 13, include information on nutrition and health habits of a sample of 315 people. One of the variables is VitaminUse, indicating
Samples of size 1000 from a population with mean 28 and standard deviation 5If random samples of the given size are drawn from a population with the given mean and standard deviation:(a) Find the
Samples of size 10 from a population with mean 6 and standard deviation 2If random samples of the given size are drawn from a population with the given mean and standard deviation:(a) Find the mean
Samples of size 40 from a population with mean 250 and standard deviation 80If random samples of the given size are drawn from a population with the given mean and standard deviation:(a) Find the
Samples of size 75 from a population with mean 60 and standard deviation 32If random samples of the given size are drawn from a population with the given mean and standard deviation:(a) Find the mean
Find endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n = 10.Assume the sample is a random sample from a distribution that is reasonably normally distributed and

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