Questions and Answers of Practice of Statistics

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100
Refer to Exercise 74.a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.b. According to the packaging, there are supposed to be 330
Refer to Exercise 41. The study also estimated that 67% of adults aged 18–29 play video games, but only 25% of adults aged 65 and older play video games.a. Explain why you do not have enough
Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60
Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.For a poll of 1600 adults, the variation due to sampling error is no
Of the 24,611 degrees in mathematics given by U.S. colleges and universities in a recent year, 70% were bachelor’s degrees, 24% were master’s degrees, and the rest were doctorates. Moreover,
Based on the P-value in Exercise 31, which of the following would be the most appropriate conclusion?a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50% of
In the sample, p̂ = 158/300 = 0.527. The resulting P-value is 0.18. What is the correct interpretation of this Pvalue?a. Only 18% of the city residents support the tax increase.b. There is an 18%
A Type I error in the context of this study occurs if the city councila. Finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn’t convincing
Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud
Statistics can help decide the authorship of literary works. Sonnets by a well-known poet contain an average of μ = 6.9 new words (words not used in the poet’s other works) and a standard
The Environmental Protection Agency (EPA) has determined that safe drinking water should contain at most 1.3 mg/liter of copper, on average. A water supply company is testing water from a new source
In the population of people in the United States, about 10% are left handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10% of students at his school
Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life threatening injuries, victims generally need medical attention
Nationally, the proportion of red cars on the road is 0.12. A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red
Television networks rely heavily on ratings of TV shows when deciding whether to renew a show for another season. Suppose a network has decided that “Miniature Golf with the Stars” will only be
You are thinking about opening a restaurant and are searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over $85,000
The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1 pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees
A student performs a test of H0: μ = 12 versus Ha: μ ≠ 12 at the α = 0.05 significance level and gets a P-value of 0.01. The student writes: “Because the P-value is small, we reject H0. The
A student performs a test of H0: p = 0.75 versus Ha: p < 0.75 at the α = 0.05 significance level and gets a P-value of 0.22. The student writes: “Because the P-value is large, we accept H0. The
Refer to Exercises 2 and 12.a. What conclusion would you make at the α = 0.01 level?b. Would your conclusion from part (a) change if a 5% significance level was used instead? Explain your
Refer to Exercises 3 and 11.a. What conclusion would you make at the α = 0.10 level?b. Would your conclusion from part (a) change if a 5% significance level was used instead? Explain your
Refer to Exercises 4 and 10. What conclusion would you make at the α = 0.05 level?Exercises 4 and 10.The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’
Refer to Exercises 1 and 9. What conclusion would you make at the α = 0.05 level?Exercises 1 and 9.Mr. Tabor believes that less than 75% of the students at his school completed their math homework
A student performs a test of H0: p = 0.3 versus Ha: p < 0.3 and gets a P value of 0.22. The student says, “This means there is about a 22% chance that the null hypothesis is true.” Explain why
A student performs a test of H0: μ = 100 versus Ha: μ > 100 and gets a P value of 0.044. The student says, “There is a 0.044 probability of getting the sample result I did by chance alone.”
Refer to Exercise 2. Yvonne finds that 96 of the 150 students (64%) say they rarely or never argue with friends. A significance test yields a P-value of 0.0291. Interpret the P-value.Exercise 2.A
Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. A significance test yields a P-value of 0.0589. Interpret the P-value.Exercise 3.One
Refer to Exercise 1. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test
a. A change is made that should improve student satisfaction with the parking situation at your school. Before the change, 37% of students approve of the parking that’s provided. The null
Refer to Exercise 4. In the study of older students’ attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.a.
a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37% of students approve of the parking that’s provided. The null
When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from 0 to 200. Higher scores indicate better
One company’s bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. A quality control inspector must check that the machine is
During the winter months, the temperatures at the Starneses’ Colorado cabin can stay well below freezing (32°F or 0°C ) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets
Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at
A Gallup poll report revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this result holds true in her large high school, so she surveys a random
Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24 laboratory rats. A 95% confidence interval for the mean blood cholesterol level μ
Stores advertise price reductions to attract customers. What type of price cut is most attractive? Experiments with more than one factor allow insight into interactions between the factors. A study
Choose a young person (aged 19 to 25) at random and ask, “In the past seven days, how many days did you watch television?” Call the response X for short. Here is the probability distribution for
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest
You have an SRS of 23 observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence
One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is thata. z can be used
Writers in some fields summarize data by giving x¯ and its standard error rather than x¯ and sx. Biologists studying willow plants in Yellowstone National Park reported their results in a table
When two lights close together blink alternately, we “see” one light moving back and forth if the time between blinks is short. What is the longest interval of time between blinks that preserves
High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI
Refer to Exercise 73.a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.b. According to the manager of the restaurant, there should
Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. To investigate, they went to their favorite pizza restaurant at 10
Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) was measured for each fly in a random sample of 49 male fruit
Carly and Maysem plan to be preschool teachers after they graduate from college. To prepare for snack time, they want to know the mean number of goldfish crackers in a bag of original-flavored
The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a
Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.a. We want to estimate the average age at which U.S. presidents
Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36 cookies and found the
Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral
A study of commuting times reports the travel times to work of a random sample of 20 employed adults in New York State. The mean is x̅ =31.25 minutes and the standard deviation is sx = 21.88
A medical study finds that x̅ =114.9 and sx = 9.3 for the seated systolic blood pressure of the 27 randomly selected adults. What is the standard error of the mean? Interpret this value in context.
Judy is interested in the reading level of a medical journal. She records the length of a random sample of 100 words. The histogram displays the distribution of word length for her sample. Determine
Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf
What critical value t* from Table B should be used for a confidence interval for the population mean in each of the following situations?a. A 90% confidence interval based on n = 12 randomly selected
Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.a. How much time do students at your school spend on the Internet?
What critical value t* from Table B should be used for a confidence interval for the population mean in each of the following situations?a. A 95% confidence interval based on n = 10 randomly selected
A home gardener likes to grow various kinds of citrus fruit. One of his mandarin orange trees produces oranges whose circumferences follow a Normal distribution with mean 21.1 cm and standard
The gardener in the previous exercise randomly selects 20 mandarin oranges from the tree and counts the number of seeds in each orange. Here are the data:a. Graph the data using a dotplot.b. Based on
A newspaper reporter asked an SRS of 100 residents in a large city for their opinion about the mayor’s job performance. Using the results from the sample, the C% confidence interval for the
Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their
Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3 percentage points to 1.5 percentage points. How should they adjust their sample size?a. Multiply the sample
A Gallup poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95% confidence level.
Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes
According to a Gallup Poll report, 64% of teens aged 13 to 17 have TVs in their rooms. Here is part of the footnote to this report:These results are based on telephone interviews with a randomly
Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence
A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or
PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to
A small pilot study estimated that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice.a. How large a
Use your interval from Exercise 40 to construct and interpret a 99% confidence interval for the total number of students at the school that the student body president can identify by name. Then use
Use your interval from Exercise 39 to construct and interpret a 90% confidence interval for the total number of seniors planning to go to the prom.Exercise 39.Tonya wants to estimate what proportion
According to a recent study by the Annenberg Foundation, only 36% of adults in the United States could name all three branches of government. This was based on a survey given to a random sample of
A 2016 survey of 1480 randomly selected U.S. adults found that 55% of respondents agreed with the following statement: “Organic produce is better for health than conventionally grown produce.”a.
Refer to Exercise 42. The study also reported that 86% of millennials included 9/11 in their top-10 list and 70% of baby boomers included 9/11.a. Explain why you do not have enough information to
A recent study asked U.S. adults to name 10 historic events that occurred in their lifetime that have had the greatest impact on the country. The most frequently chosen answer was the September 11,
A Pew Research Center report on gamers and gaming estimated that 49% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based
The student body president of a high school claims to know the names of at least 1000 of the 1800 students who attend the school. To test this claim, the student government advisor randomly selects
Tonya wants to estimate what proportion of her school’s seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.a.
Refer to Exercise 35. Calculate and interpret the standard error of p̂ for these data.Exercise 35.According to a recent Pew Research Center report, many American adults have made money by selling
Refer to Exercise 36. Calculate and interpret the standard error of p̂ for these data.Exercise 36.What proportion of students are willing to report cheating by other students? A student project put
What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students
According to a recent Pew Research Center report, many American adults have made money by selling something online. In a random sample of 4579 American adults, 914 reported that they earned money by
When constructing a confidence interval for a population proportion, we check that both np̂ and n(1 − p̂) are at least 10.a. Why is it necessary to check this condition?b. What happens to the
When constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.a. Why is it necessary to check this condition?b. What
The small round holes you often see in seashells were drilled by other sea creatures, who ate the former dwellers of the shells. Whelks often drill into mussels, but this behavior appears to be more
A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.Check whether each of the
Glenn wonders what proportion of the students at his college believe that tuition is too high. He interviews an SRS of 50 of the 2400 students and finds 38 of those interviewed think tuition is too
Latoya wants to estimate the proportion of the seniors at her boarding school who like the cafeteria food. She interviews an SRS of 50 of the 175 seniors and finds that 14 think the cafeteria food is
How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs:a. Construct a scatterplot using brother’s height as the
living near power lines cause leukemia in children? The National Cancer Institute spent 5 years and $5 million gathering data on this question. The researchers compared 638 children who had leukemia
You have measured the systolic blood pressure of an SRS of 25 company employees. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which
In a poll conducted by phone,I. Some people refused to answer questions.II. People without telephones could not be in the sample.III. Some people never answered the phone in several calls. Which of
After deciding on a 95% confidence level, the researcher is deciding between a sample of size n = 500 and a sample of size n = 1000. Compared with using a sample size of n = 500, a confidence
The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared with a 95% confidence interval, a 99% confidence interval will bea. Narrower and would involve a larger

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