Questions and Answers of Introduction To Statistical Investigations

Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
According to the Pew Research Center, in 2015, 19% of all American adults had Twitter accounts. Suppose this is true now. a. If a random sample of 500 Americans is taken, use the normal
In Exercise 11.2.11, are the events that a randomly chosen person uses Facebook and a randomly chosen person uses Instagram mutually exclusive? What would have to be true about Facebook and Instagram
Repeat Exercise 11.1.10 for the approximate probability that at least one baby is returned to the right mother.Data from Exercise 11.1.10Use the Random Babies applet to investigate what happens as
Repeat Exercise 11.1.10 for the approximate probability that at least one baby is returned to the right mother.Data from Exercise 11.1.10Use the Random Babies applet to investigate what happens as
Recall the probability distribution for nonfamily household size given in Exercise 11.4.9. a. What was the mean nonfamily household size in the United States in 2016? b. What was the
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. Suppose you plan always to bet $1 on
As estimated by the Pew Research in 2016, the probability a randomly chosen American adult uses Instagram is 0.28, the probability a randomly chosen American adult uses Twitter is 0.21, and the
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Instagram are shown in the following two-way table. a. Use
Airlines will often overbook their flights (selling more tickets than they have seats) because not all customers show up for some flights. The proportion that doesn’t show up varies greatly,
Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
Recall the probability distribution for the number of people in a family of four who will draw their own name given in Exercise 11.4.10. a. What is the expected value for the number of people
About 20% of the world’s population lives in China. Suppose this is exactly true. a. If a random sample of 1,000 people in the world is chosen, use the normal approximation to the binomial
Recall the scenario of drawing names to decide who would give a Christmas present in a family of four in Exercise 11.4.10. Suppose a family of three uses the same method. a. Create a probability
The SAT® and ACT® are two common standardized tests that high school students take as part of college applications. In 2016 the mean composite SAT score was 1,020 with a standard deviation of 194.
As estimated by the Pew Research Center in 2016, the probability a randomly chosen American adult uses Instagram is 0.28, the probability a randomly chosen American adult uses Twitter is 0.21, and
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. If a person is randomly chosen
Recall Exercise 11.5.11 on betting on the number 23 on the roulette wheel. a. Write out the probability distribution for betting $1 on red twice. b. Find the mean of your probability
Random ice cream prices: As in Example 11.1, consider rolling many (fair six-sided) dice, where price is still determined as the largest number followed by the smallest number (in cents). Answer the
The SAT® is a common standardized test that high school students take as part of college entrance. In 2016 the mean composite SAT score was 1020 with a standard deviation of 194. These scores are
A Canadian study (Janssen et al., 2007) looked at the birthweights of babies of different ethnic groups. Their sample of newborns (born after 39 weeks) of European descent had a mean length of 50.5
Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
In Exercise 11.2.13, are the events that a randomly chosen person uses Twitter and a randomly chosen person uses Instagram complements of each other? What would have to be true about Twitter and
Consecutive numbers: a. Determine the (exact, theoretical) probability that rolling a pair of fair six-sided dice results in consecutive numbers, such as (1, 2) or (5, 4).b. Suppose that the
Suppose that a family has three children, and each child is equally likely to be a boy or a girl. a. Write out the sample space of 8 possible outcomes. (For example, use the notation B1G2B3 to
The example in this section described a prize wheel divided into 12 equal-sized sectors where 8 are marked no prize, 3 are marked win $1, and 1 is marked win $25. We will call this wheel A. Suppose
In Exercise 11.3.14, are the events “a randomly chosen person uses Twitter” and “a randomly chosen person uses Instagram” independent? What would have to be true about Twitter and Instagram
In 2014, Jack in the Box® restaurants conducted a game called the Munchie Peel Instant Win Game® where you could peel a sticker off one of their meal boxes and possibly win a prize. They claimed
The ACT® is a common standardized test that high school students take as part of college entrance. In 2016 the mean composite ACT score was 21.0 with a standard deviation of 5.4. These scores are
In 2018, Tim Hortons® restaurants conducted a game called Roll up the Rim to Win® where you could roll up the rim of one of their medium-sized or larger beverage paper cups (to reveal something
About 10% of the population is left-handed. Let’s suppose this is exactly true and you are randomly choosing people from the population until you get a left-hander. a. What is the probability
Repeat Exercise 11.1.11 for the average number of babies that are returned to the right mother.Data from Exercise 11.1.11Repeat Exercise 11.1.10 for the approximate probability that at least one baby
Recall Exercise 11.5.10 on betting on red on the roulette wheel. a. Write out the probability distribution of the payout for betting $1 on red twice. b. Find the mean of your probability
Human blood types can be separated into four categories: A, B, AB, and O. The following partial distribution gives the approximate proportion in which these types occur in the U.S.
According to the Census Bureau, 33.4% of Americans 25 years old and older had a college degree in 2016. a. Use the One Proportion applet to do a simulation (with at least 10,000 repetitions) to
The Canadian study described in Exercise 11.5.14 that looked at the birthweights of babies of different ethnic groups also had a sample of newborns of South Asian descent that had a mean length of
In 2008 a college was shut down because of high rates of norovirus in the student population. The following table gives the numbers of male and female students who did and did not contract the virus
In 2008 a college was shut down because of high rates of norovirus in the student population. The following table gives the numbers of male and female students who did and did not contract the virus
Suppose that a family has four children, and each child is equally likely to be a boy or a girl. a. Write out the sample space of 16 possible outcomes. (For example, use the notation B1G2G3B4 to
Reconsider the prize wheels described in the Example 11.4 and in Exercise 11.4.15. The average distance the outcomes are from the expected value for the wheel from the example (wheel A) can be
In Exercise 11.6.15 about the Munchie Peel Instant Win Game®: a. What is the expected number of winning stickers for those that buy four meals? b. What is the standard deviation for the
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. Heights of females in the United States are
An elevator near the office of one of the authors contains a sign that says its maximum capacity is 4,000 pounds or 26 people. It makes one wonder (well, at least it made one author wonder!), what is
A statistics instructor gave a 10-point quiz in which the mean was 7.72 with a standard deviation of 2.45. Suppose the instructor, being in a generous mood, adjusts all the scores by adding a point
A teacher was on a committee consisting of four male and two female teachers. Two members of the committee were chosen to do some extra work, and it turned out that both females were chosen. The
The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let So represent the event a student chosen is a sophomore and let F represent
Suppose a litter of puppies has 3 males and 3 females. Suppose two puppies are chosen at random and we let X be the number of male puppies chosen. a. Create a probability distribution for
Use data from the table in Exercise 11.2.16 about the norovirus to answer the following questions. a. What is the value of P((Y or F)c) and what does it mean in the context of this
The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let S represent the event a student chosen is a sophomore and let F represent
Some marathons are so popular that they use lotteries to determine who can run in them. In the 2016 New York City Marathon, about 23% of those who registered to enter through the lottery were
Heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches. a. What is the probability that a randomly
A statistics instructor gave a 10-point quiz in which the mean was 8.28 with a standard deviation of 1.58. Suppose the instructor, being a mean ogre, adjusts all the scores by dividing them all by 2
A 19-foot Scout fishing boat contains a U.S. Coast Guard label for maximum capacity. It states that the maximum capacity is 6 persons or 1,000 pounds (not including gear). a. The average weight
Reconsider Exercise 11.1.17. Let’s call the male members of the committee Abe, Bob, Carlos, and Dante. Let’s call the female members Ellen and Fiona. a. List the sample space of all possible
In a certain college statistics class, 61% of the students are female and 39% are male. Of the females, 40% are regular coffee drinkers. Of the males, 30% are regular coffee drinkers. a. What
Suppose you are asked to play a game where you roll a single six-sided die. If it lands on a 6, you win $10. If it doesn’t land on 6, you roll again. If it lands on a 6, the second time you win $6.
In Exercise 11.6.17 about getting into the New York City Marathon: a. What is the mean number of times people get accepted if they enter the lottery for 5 years? b. What is the mean number
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. a. What is the probability that a randomly chosen
Heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches. a. What is the probability that a randomly
In Exercise 11.5.17 the instructor divided all the scores by 2 and then subtracted 1 point from each. Suppose a second method is to first subtract 1 from the scores and then divide by 2. a. How
Use the table in Exercise 11.2.18 on the distribution of students to answer the following questions. a. What proportion of all students are male? b. What proportion of all students are both
The NPR show Wait Wait ... Don’t Tell Me gives its guests a three-question quiz in which they have three answer choices for each question. The questions are so obscure that the guest typically must
Unfinished game: Suppose that Heather and Tom play a game that involves a series of coin flips. They agree that if 5 heads occur before 5 tails do, then Heather wins the game. But if 5 tails occur
Reconsider Exercise 11.1.19. a. Describe how you could use a simulation analysis to approximate the probability that Heather would win the game if it were finished. b. Use the following
It is estimated that 42% of all Americans have type A blood. Suppose two Americans are randomly selected (so the probability of one having type A blood is independent of the other). Find the
In 1938 Dr. Frank Benford, a physicist at General Electric, noticed that, given a list of numbers, more numbers started with the digit 1 than any other digit. He analyzed 20,222 sets of numbers
Recall Exercise 11.6.17 about getting into the New York City Marathon. You plan to enter until you get in and then won’t apply again. What is the smallest number of times you would have to enter so
The heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches and the heights of males are approximately
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. a. What is the probability that a randomly chosen
A sample of 65 healthy males in a vaccine trial had a mean body temperature of 98.105° Fahrenheit with a standard deviation of 0.699° Fahrenheit. If all these temperatures were converted to degrees
In Exercise 11.3.19 we saw that 42% of all Americans have type A blood. Assume five Americans are chosen at random. a. What is the probability that all of them have type A blood?b. What is the
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. The wheel is spun and a ball will
According to the Kaiser Family Foundation, the proportions of the U.S. population who have various types of health insurance in 2015 are as shown in the table a. Find the proportion of people
In a bone density test, one of the results is given as a z-score. This is simply the number of standard deviations above or below the average bone density of someone of the same sex and age as the
To answer the following questions, we assume the probability that a family has a boy or a girl is the same (0.50) and that a family will have three children. a. Write out the sample space by
Are metal bands used for tagging harmful to penguins? In Nature, researchers Saraux et al. reported the results of an investigation done to answer this question using a sample of 100 penguins near
A sample of 65 healthy females in a vaccine trial had a mean body temperature of 98.394° Fahrenheit with a standard deviation of 0.743° Fahrenheit. If all these temperatures were converted to
Suppose that a basketball player named Jose makes 60% of his free throws, and Kayla makes 70% of her free throws. Each player attempts 100 free throws at the end of practice one day. Regard these as
Reconsider the Exercises 11.1.19 and 11.1.20. a. Suppose that the rules were changed so that the winner is the first to reach 10 heads or tails, rather than 5. (Continue to assume that the game
A string of cheap Christmas lights contains 10 lights. Each individual light has a 0.10 probability of failing during the Christmas season. Assume the lights fail independently of each other. a.
Reconsider the roulette wheel description in Exercise 11.6.20. If you bet $1 on red and the ball lands on a red number, you will get your $1 back plus another $1. If the ball does not land on a red
Reconsider Exercise 11.8.20. Describe how the probability that ((p(vector)Kayla − p(vector)Jose > 0) would change if: a. The sample sizes were larger. b. Kayla’s probability of
Suppose two parents have blood genotypes such that the probability that any of their children have blood type A is 0.75. a. If they have 5 children: i. What is the probability that all have
Suppose that Karen and John get together to grade their students’ exams. The time required for Karen to grade a question on a student’s exam is normally distributed with mean 90 seconds and
According to a study done in the United Kingdom, a male’s probability of death from lung cancer during his lifetime is 0.077. For someone that is a heavy smoker (at least 25 cigarettes a day), that
The two distributions for Exercise 2.2.14 are the mean length of words from samples of 10 words and 30 words from the Gettysburg Address. Which distribution comes from samples of size 10 and which
Recall Exercise 3.4.41 about the size of a sample needed for a margin of error of at most 0.03. What sample size is needed to have a margin of error of at most 0.03 for a 99% confidence interval? Use
You often see margins of errors in polling results listed as ±3%. What sample size do you need to have a margin of error of at most 0.03 for a 95% confidence interval? To answer this question, set
Refer to Exercise 8.2.25 on accuracy in surveys. Another way to measure accuracy of responses is whether people round when giving numerical answers. The researchers considered a number to be rounded
Data were gathered on 106 statistics students from a Midwestern college on variables including the sex of the respondent and whether they had eaten breakfast that morning.If there were no association
What are the observational units?Social psychologists throughout the years have shown that an aggression–sexuality link exists not only in various animal species but also in humans. Dutton and Aron
Recall Exercise 7.3.34 about comparing ratings of intensity for male-named hurricanes and female-named hurricanes. a. Put the data into the Matched Pairs applet to find the sample mean, sample
Reconsider Exercises 8.1.23–8.1.25 on cell phone and smartphone ownership. We considered our population to be that of all adults in the United States. Now suppose we want the population to be all
Two samples of Facebook users chosen by the Pew Research Center (one in 2019 and one in 2013) were asked how often they visit or use Facebook. The results are shown in the two-way table. We will
Bergmann’s rule (named after German biologist Carl Bergmann) is an ecogeographical rule that states that within a species, specimens will tend to be larger if they are from cooler climates or more
Given the information in this partial ANOVA table, what is the value of the F-statistic? A. 0.76 B. 2.31 C. 7.59 D. 10.02 E. 17.53 Source
Two researchers (Veronica and Bella) are working separately to investigate whether reaction time (seconds) is associated with the presence and type of music that is playing in the background. Summary
When surveys are administered, it is hoped that the respondents give accurate answers. Does the mode of survey delivery affect this? American researchers investigated this question (Schober et al.,
Recall Exercise 8.1.30 on accuracy of survey responses. Another way to measure accuracy of responses is whether people round when giving numerical answers. The researchers considered a number to be

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