Questions and Answers of Practice of Statistics

Write a few sentences comparing the distributions of average English grade for light and heavy readers.Do students who read more books for pleasure tend to earn higher grades in English? The boxplots
Which of the following is false?a. A chi-square distribution with k degrees of freedom is more rightskewed than a chi-square distribution with k+1 degrees of freedom.b. A chi-square distribution
The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?a. Because 0.0129 is less than α = 0.05
The chi-square test statistic isa.b.c.d.e.The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each
An appropriate null hypothesis to test whether the food choices are equally popular isa. H0: μ = 25 where μ = the mean number of students that prefer each type of food.b. H0: p = 0.25 where p = the
When a fair coin is flipped, we all know that the probability the coin lands on heads is 0.50. However, what if a coin is spun? According to the article “Euro Coin Accused of Unfair Flipping” in
Use your calculator’s RandInt function to generate 200 digits from 0 to 9 and store them in a list.a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether
Statistics teacher Jason Molesky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: “The original flavor blend for the
Gregor Mendel (1822–1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or
The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random
Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29%
Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other
The principal in Exercise 7 also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the
The paper “Linkage Studies of the Tomato” (Transactions of the Canadian Institute, 1931) reported the following data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf
Biologists wish to mate pairs of fruit flies having genetic makeup RrCc, indicating that each has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one
Kellogg’s Froot Loops cereal comes in six colors: orange, yellow, purple, red, blue, and green. Charise randomly selected 120 loops and noted the color of each. Here are her data:Do these data
A school’s principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time
Refer to Exercise 2.a. Confirm that the expected counts are large enough to use a chisquare distribution to calculate the P-value. What degrees of freedom should you use?b. Use Table C to find the
Refer to Exercise 1.a. Confirm that the expected counts are large enough to use a chisquare distribution to calculate the P-value. What degrees of freedom should you use?b. Use Table C to find the
For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.a. χ2 = 4.49, df = 5b. χ2 = 4.49, df = 1Table C Table C Chi-square
For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.a. χ2 = 19.03, df = 11b. χ2 = 19.03, df = 3Table C Table C Chi-square
Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 slots—18 red, 18 black, and 2 green. In one casino, managers record data from a random sample
A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% Brazil nuts. To test this claim, a qualitycontrol inspector takes a random
What we really want to know is whether coached students improve more than uncoached students, on average, and whether any advantage is large enough to be worth paying for. Use the information above
Let’s first ask if students who are coached increased their scores significantly, on average.a. You could use the information on the Coached line to carry out either a two-sample t test comparing
a. A city planner wants to determine if there is convincing evidence of a difference in the average number of cars passing through two different intersections. He randomly selects 12 times between
a. Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said
The P-value for a test of versus is 0.227. Which of thefollowing is the correct interpretation of this P-value?a. The probability that is 0.227.b. Given that the true mean difference
A 95% confidence interval for is given bya.b.c.d.e.Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers
A study of the impact of caffeine consumption on reaction time was designed to correct for the impact of subjects’ prior sleep deprivation by dividing the 24 subjects into 12 pairs on the basis of
There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ, on average? You apply both methods to each fish in a random sample of 18 carp
Refer to Exercise 77. The pilot suspects that the Dubai-to- Doha outbound flight typically takes longer. If so, the difference in flight times will be positive on more days than it is negative.
Can students throw a baseball farther than a softball? To find out, researchers conducted a study involving 24 randomly selected students from a large high school. After warming up, each student
In each of the following settings, decide whether you should use two sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean
In each of the following settings, decide whether you should use two sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean
Refer to Exercise 88.a. Construct and interpret a 90% confidence interval for the true mean difference. If you already defined parameters and checked conditions in Exercise 88, you don’t need to do
Refer to Exercise 87.a. Construct and interpret a 99% confidence interval for the true mean difference. If you already defined the parameter and checked conditions in Exercise 87, you don’t need to
Do people behave differently on Friday the 13th? Researchers collected data on the number of shoppers at a random sample of 45 grocery stores on Friday the 6th and Friday the 13th in the same month.
Does listening to music while studying help or hinder students’ learning? Two statistics students designed an experiment to find out. They selected a random sample of 30 students from their
Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent
Many people think it’s faster to order at the drive-thru than to order inside at fast-food restaurants. To find out, Patrick and William used a random number generator to select 10 times over a
Refer to Exercise 78. Explain why it is not appropriate to perform a paired t test about the true mean difference in literacy rates in Islamic countries.Exercise 78.Do males have higher
Refer to Exercise 77. Explain why it is not appropriate to perform a paired t test about the true mean difference (Outbound − Return) in flight times between Dubai and Doha. See Exercise 94 for an
A bank wonders if omitting the annual credit card fee for customers who charge at least $2400 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of
Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool
Refer to Exercise 76. Construct and interpret a 95% confidence interval for the true mean difference (Bottom – Top) in the zinc concentrations of the wells in this region.Exercise 76.Trace metals
Refer to Exercise 75. Construct and interpret a 95% confidence interval for the true mean difference (Weight – Groove) in the estimates of tire wear using these two methods in the population of
Do males have higher literacy rates than females, on average, in Islamic countries? The following table shows the percent of men and women who were literate in 24 largely Muslim nations at the time
Emirates Airline offers one outbound flight from Dubai, United Arab Emirates, to Doha, Qatar, and one return flight from Doha to Dubai each day. An experienced Emirates pilot suspects that the
Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and
Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of
Researchers in Spain interviewed 7725 13-year-olds about their homework habits—how much time they spent per night on homework and whether they got help from their parents or not—and then had them
Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals
Based on the P-value in Exercise 71, which of the following must be true?a. A 90% confidence interval for will contain 0.b. A 95% confidence interval for will contain 0.c. A 99%
a. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting a difference in sample means equal to the one observed in this study.b.
Which of the following describes a Type II error in the context of this study?a. Finding convincing evidence that the true means are different for males and females, when in reality the true means
Does sleep deprivation linger for more than a day? Researchers designed a study using 21 volunteer subjects between the ages of 18 and 25. All 21 participants took a computer-based visual
A random sample of 30 words from Jane Austen’s Pride and Prejudice had a mean length of 4.08 letters with a standard deviation of 2.40. A random sample of 30 words from Henry James’s What Maisie
Do external rewards—things like money, praise, fame, and grades promote creativity? Researcher Teresa Amabile suspected that the answer is no, and that internal motivation enhances creativity. To
A company that makes hotel toilets claims that its new pressure assisted toilet reduces the average amount of water used by more than 0.5 gallon per flush when compared to its current model. To test
In a pilot study, a company’s new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing evidence that the mean cholesterol reduction with the new drug
Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers compared a random sample of 47 breast-feeding
An educator believes that new reading activities in the classroom will help elementary school pupils improve their reading ability. She recruits 44 third-grade students and randomly assigns them into
Refer to Exercise 59.a. Construct and interpret a 95% confidence interval for the difference between the true means. If you already defined parameters and checked conditions in Exercise 59, you
Refer to Exercise 60.a. Construct and interpret a 99% confidence interval for the difference between the true means. If you already defined parameters and checked conditions in Exercise 60, you
Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period
To see if fish oil can help reduce blood pressure, males with high blood pressure were recruited and randomly assigned to different treatments. Seven of the men were assigned to a 4-week diet that
In many parts of the northern United States, two color variants of the Eastern Gray Squirrel— gray and black—are found in the same habitats. A scientist studying squirrels in a large forest
Do birds learn to time their breeding? Blue titmice eat caterpillars. The birds would like lots of caterpillars around when they have young to feed, but they must breed much earlier. Do the birds
Refer to Exercise 54.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
Refer to Exercise 53.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
For a statistics class project, Jonathan and Crystal held an ice-cream eating contest. They randomly selected 29 males and 35 females from their large high school to participate. Each student was
Student researchers Adam, Edward, and Kian wondered if music would affect performance for certain tasks. To find out, they had student volunteers sort a shuffled set of 26 playing cards by face value
Many students at Matt’s school claim they can think more clearly while listening to their favorite kind of music. Matt believes that music interferes with thinking clearly. To find out which is
As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed separate random samples of Hispanic and Anglo customers
A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of small nests and the other of large nests. Then she weighs one egg (chosen
Catherine and Ana wanted to know if student athletes (students on at least one varsity team) have faster reaction times than non-athletes. They took separate random samples of 33 athletes and 30
In a study of heart surgery, one issue was the effect of drugs called beta blockers on the pulse rate of patients during surgery. The available subjects were randomly assigned into two groups. One
College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of
Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Researchers believe that over time, the lengths of the flowers and the forms of the
Observational studies suggest that moderate use of alcohol by adults reduces heart attacks and that red wine may have special benefits. One reason may be that red wine contains polyphenols,
Mary was interested in comparing the mean word length in articles from a medical journal and an airline’s in-flight magazine. She counted the number of letters in the first 400 words of an article
How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we chose independent random samples of 50 students from each
For their final project, a group of AP® Statistics students wanted to compare the texting habits of males and females. They asked a random sample of students from their school to record the number
How many pairs of shoes do teenagers have? To find out, a group of AP® Statistics students conducted a survey. They selected a random sample of 20 female students and a separate random sample of 20
Refer to Exercise 38.a. Find the probability of getting a difference in sample means x¯M−x¯Wthat’s greater than 2 inches.b. Should we be surprised if the sample mean height for the young men is
Refer to Exercise 37.a. Find the probability of getting a difference in sample means x¯M−x¯B that’s less than 0 mg/dl.b. Should we be surprised if the sample mean cholesterol level for the
The heights of young men follow a Normal distribution with mean μM = 69.3 inches and standard deviation σM = 2.8 inches. The heights of youngwomen follow a Normal distribution with mean
The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean μM =188 milligrams per deciliter (mg/dl) and standard deviation σM = 41
a. Explain what the value of r2 tells you about how well the least squares line fits the data.b. The mean age of the students’ cars in the sample was x¯ = 5 years. Find the mean mileage of the
a. What is the equation of the least-squares regression line? Be sure to define any symbols you use.b. Interpret the slope of the least-squares line.c. One student reported that her 10-year-old car
In an experiment to learn whether substance M can help restore memory, the brains of 20 rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10 rats
Which of the following is the correct margin of error for a 99% confidence interval for the difference in the proportion of male and female college students who worked for pay last summer?a.b.c.d.e.A
The researchers report that the results were statistically significant at the 1% level. Which of the following is the most appropriate conclusion?a. Because the P-value is less than 1%, fail to
Let pM and pF be the proportions of all college males and females who worked last summer. The hypotheses to be tested area. H0: pM − pF = 0 versus Ha: pM − pF ≠ 0.b. H0:
You may have heard that Botox (botulinum toxin type A) is used for cosmetic surgery, but could it have other beneficial uses? A total of 31 patients who suffered chronic low-back pain were randomly
Does providing additional information affect responses to a survey question? Two statistics students decided to investigate this issue by asking different versions of a question about texting and
A study reported in the medical journal Fertility and Sterility sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant. A total of 160 healthy
Two hundred women who were about to undergo IVF served as subjects in an experiment. Each subject was randomly assigned to either a treatment group or a control group. Several people (called
Refer to Exercise 24.a. Construct and interpret a 95% confidence interval for the difference between the true proportions. Assume that the conditions for inference are met.b. Explain how the

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