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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

A balanced coin is flipped 100 times. By the law of large numbers:a. There will almost certainly be exactly 50 heads and 50 tails.b. If we got 100 heads in a row, almost certainly the next flip will
Which of the following is always true?a. If A and B are independent, then they are also disjoint.b. P(AΙB) + P(AΙBc) = 1c. If P(AΙB) = P(BΙA), then A and B are independent.d. If A and B are
Choose ALL correct responses. For two events A and B, P(A) = 0.5 and P(B) = 0.2. Then P(A or B) equalsa. 0.10, if A and B are independentb. 0.70, if A and B are independentc. 0.60, if A and B are
Of the participants at a conference, 50% attended breakfast, 90% attended dinner, and 40% attended both breakfast and dinner. Given that a participant attended breakfast, find the probability that
A couple has five children, all girls. They are expecting a sixth child. The father tells a friend that by the law of large numbers the chance of a boy is now much greater than 1/2. Comment on the
In Example 16, we estimated the probability of winning the game was 0.65.a. If you conducted another 20 simulations of this game, what probability of winning would you expect to get?b. The simulation
A standard deck of poker playing cards contains four suits (clubs, diamonds, hearts, and spades) and 13 different cards of each suit. During a hand of poker, 5 of the 52 cards have been exposed. Of
Petra Kvitova of the Czech Republic won the 2014 Wimbledon Ladies’ Singles Championship. In the final game against Eugenie Bouchard of Canada she had 41 first serves, of which 28 were good, and
Are people happy in their romantic relationships? The table shows results from the 2012 General Social Survey for adults classified by gender and happiness.a. Estimate the probability that an adult
A 2014 Gallup poll reported that 27% of people in the United States are obese (having a body mass index score of 30 or more). Blacks have the highest obesity rate at 35%, whereas Asians have the
Table 5.3 on audit status and income follows. Show how to find the probability of:a. Being audited, given that the taxpayer is in the lowest income category.b. Being in the lowest income category,
A 2014 article from Business Insider (http://www.business insider.com/department-of-justice report- shows-high-recidivism-rate-2014-4) discusses recidivism rates in the United States. Recidivism is
You are the director of newspaper sales for the local paper. Each customer has signed up for either weekday delivery or weekend delivery. You record whether he or she received the delivery as Y for
At the local cell phone store, the probability that a customer who walks in will purchase a new cell phone is 0.2. The probability that the customer will purchase a new cell phone protective case is
Every year the insurance industry spends considerable resources assessing risk probabilities. To accumulate a risk of about one in a million of death, you can drive 100 miles, take a cross country
Some friends are playing a game in which two six-sided dice are rolled (craps, Settlers of Catan, etc.). One of them exclaims, “Since the sum of the dice is between 2 and 12, there is a one in
Use the web app Random Numbers (go to the tab that says Coin Flips) on the book’s website or other software (such as random.org/coin) to illustrate the long-run definition of probability by
You are asked to use your best judgment to estimate the probability that there will be a nuclear war within the next 10 years. Is this an example of relative frequency or subjective definition of
Before the first human heart transplant, Dr. Christiaan Barnard of South Africa was asked to assess the probability that the operation would be successful. Did he need to rely on the relative
A pollster agency wants to estimate the proportion of citizens of the European Union who support same-sex unions. She claims that if the sample size is large enough, she does not need to worry about
Consider a random number generator designed for equally likely outcomes. Which of the following is not correct, and why?a. For each random digit generated, each integer between 0 and 9 has
The powerrank.com website (http:// thepowerrank.com/2014/06/06/world-cup-2014-winprobabilities- from-the-power-rank/) listed the probability of each team to win the 2014 World Cup in soccer as
The American Heart Association reports that a total cholesterol score of 240 or higher represents high risk of heart disease. A study of postmenopausal women reported a mean of 220 and standard
Exercise 6.28 mentioned that in the United States, birth weight of boys is approximately normal, with mean 3.41 kg and standard deviation 0.55 kg. For girls, the birth weight is also approximately
A collector is interested in two paintings by the same artist available at an auction. She plans to bid $3,000 for the first painting auctioned off and $2,000 for the second. She estimates that the
Four of the 20 students (20%) in a class are fraternity or sorority members. Five students are picked at random. Does X = the number of students in the sample who are fraternity or sorority members
For the binomial distribution, the number of trials n is a fixed number. Let X denote the number of girls in a randomly selected family in Canada that has three children. Let Y denote the number of
A study at the Harvard School of Public Health found that 44% of 10,000 sampled college students were binge drinkers. A student at the University of Minnesota plans to estimate the proportion of
Go to the Inference for a Mean web app, accessible on the book’s website. Select the Explore Coverage tab and keep the default skewed shape for the population distribution as well as the default
Find the margin of error for estimating the population mean when the sample standard deviation equals 100 for a sample size of 25, using confidence levels (i) 95% (ii) 99%. What is the
Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of a. 25b. 100. What is the
The General Social Survey asks respondents to rate their political views on a seven-point scale, where 1 = extremely liberal, 4 = moderate, and 7 = extremely conservative. A researcher analyzing data
For the FL Student Survey data file on the book€™s website, software reports the results for responses on the number of times a week the subject reads a newspaper:a. Is it plausible that
For the question about e-mail in the previous exercise, the 14 females in the GSS of age at least 80 had the responses 0, 0, 0, 0, 1, 1, 1, 2, 2, 6, 6, 7, 7, 10.a. Using the web app, software or a
When the GSS asked n = 1050 people in 2012, €œAbout how many hours per week do you spend sending and answering e-mail?€ (EMAILHR), the summary statistics were xÌ… =
Example 6 mentioned closing prices for listings of the iPhone 5s on eBay. If you don€™t feel comfortable bidding (or can€™t wait until a listing has ended), you can often purchase
Exercise 8.7 reported heights (in mm) of 55.5, 60.3, 60.6, 62.1, 65.5, and 69.2 for six seedlings fourteen days after germination.a. Using the web app, software or a calculator, verify that the 95%
One feature smartphone manufacturers use in advertising is the amount of time one can talk before recharging the battery. Below are 13 values from a random sample of the talk-time (in minutes) of
Using Table B, the web app, software or a calculator, report the t-score that you multiply by the standard error to form the margin of error for aa. 95% confidence interval for a mean with 5
Refer to the previous exercise. For the 530 males in the sample who gave a numeric response from 0 to 6, the mean was 2.51 and the standard deviation was 0.87.a. Find the point estimate of the
The 2012 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” The 590 females who gave a numeric response from 0 to 6 had a median of 2, mean of
Repeat the simulation from Activity 2, but this time simulate 1000 confidence intervals (repeatedly press the Draw Sample(s) button after selecting 100 as the number of samples to generate until you
A national survey by the Pew Research Center (www.people-press.org), conducted May 1-5, 2013, among 1,504 adults, finds that support for same-sex marriage continues to grow. It states, “For the
In a 2014 Consumer Reports article titled, “The High Cost of Cheap Chicken,” the magazine reported that out of 316 chicken breasts bought in retail stores throughout the United States, 207
In Exercise 8.18, it was stated that 72% of the 2113 adults surveyed in a Harris poll believed that stem cell research has merit. In the same study, only 58% of those describing themselves as
A Harris poll of a random sample of 2250 adults in the United States in 2013 reported that 74% believe in God, 68% believe in heaven, 58% believe in hell, and 42% believe in ghosts.4 (Interestingly,
Which z-score is used in a(a) 90%, (b) 98%,(c) 99.9% confidence interval for a population proportion?
In the 2012 General Social Survey, respondents were asked whether they favored or opposed the death penalty for people convicted of murder. Software shows results Here, X refers to the number of the
In a clinical study (the same as mentioned in Example 4), 3900 subjects were vaccinated with a vaccine manufactured by growing cells in fertilized chicken eggs. Over a period of roughly 28 weeks, 24
A Gallup poll of 2000 Russians taken between April and June 2014 (after the Olympic games in Russia and the annexation of the Crimean peninsula) showed that 83% approved of President Putin’s
Conduct a search to find a newspaper or magazine article that reported a margin of error. If you prefer, use the Internet for the search.a. Specify the population parameter, the value of the sample
The Google Play app store for smartphones offers hundreds of games to download for free or for a small fee. The ones for which a fee is charged are called paid games. For a random sample of five paid
In 2014, news reports worldwide alleged that the U.S. government had hacked German chancellor Angela Merkel’s cell phone. A Pew Research Center survey of German citizens at about that time asked
A recent study from Nielsen (available from nielsen.com; search for “The Cross-Platform Report”) took a sample to investigate how video on demand and other subscription-based services (such as
The formula Ïƒ/ˆšn for the standard deviation of x actually is an approximation that treats the population size as infinitely large relative to the sample size n. The exact
Suppose x = 1 with probability p, and x = 0 with probability (1 - p). Then, x is the special case of a binomial random variable with n = 1, so that With n trials, using the formula s>1n for a
Under the null hypothesis H0: p1= p2of equal population proportions, the standard error for the difference in the two sample proportions mentioned on page 494 reduces to se0= ˆš(b + c)/n2,
Refer to Example 12, which compared two groups of seven dogs each in terms of their time interacting with their owners. Figure 10.10 showed the sampling distribution by considering all possible
Suppose there is a higher percentage of successes with Treatment A than with Treatment B at a clinic in Rochester, and there is a higher percentage of successes with Treatment A than with Treatment B
A 2013 survey by the Pew Research Center asked whether there have been times in the past year the respondent has been unable to afford food. Of advanced economies, the country with the second highest
If a 95% confidence interval for (μ1 - μ) contains only positive numbers, then we can conclude that both μ1 and μ2 are positive.
If the sample proportions in Example 4 comparing cancer death rates for aspirin and placebo had sample sizes of only 1000 each, rather than about 11,000 each, then the 95% confidence interval for (p1
A study compares the population mean annual incomes for Hispanics (μ1) and for whites (μ2) having jobs in construction, using a 95% confidence interval for μ1 - μ2. Choose the best correct
Suppose that a 99% confidence interval for the difference p1 - p2 between the proportions of men and women in California who are alcoholics equals (0.02, 0.09). Choose the best correct choice.a. We
In Western Australia, handheld cell phone use while driving has been banned since 2001, but hands-free devices are legal. A study (published in the British Medical Journal in 2005) of 456 drivers in
The following data refer to a random sample of prize money earned by male and female skiers racing in the 2014/2015 FIS world cup season (in Swiss Franc).Males: 89000, 179000, 8820, 12000, 10750,
In the previous exercise, explain how the result of the 95% confidence interval in part b corresponds to the result of the decision using significance level 0.05 in part c.Previous exerciseIn 2014,
Refer to the previous exercise.a. Run a t test and report the P-value for the two-sided alternative hypothesis.b. Using a significance level of 0.10, are the decisions based on the t test and based
A t test for a mean uses a sample of 15 observations. Find the t test statistic value that has a P-value of 0.05 when the alternative hypothesis is a) Ha: μ ≠ 0, b) Ha: μ >
When the 583 female workers in the 2012 GSS were asked how many hours they worked in the previous week, the mean was 37.0 hours, with a standard deviation of 15.1 hours. Does this suggest that the
Many students brag that they have more than 100 friends on Facebook. For a class project in 2014, a group of students asked a random sample of 13 students at Williams College who used Facebook about
In Exercise 9.25, a fast-food chain compared two ways of promoting a turkey burger. In a separate experiment with 10 pairs of stores, the difference in the month€™s increased sales between
A significance test about a proportion is conducted using a significance level of 0.05. The test statistic equals 2.58. The P-value is 0.01.a. If H0 were true, for what probability of a Type I error
Example 6, in testing H0: p = 0.5 against Ha: p < 0.5, analyzed whether those opposing increased use of fracking are in the minority. In the words of thatexample, what would be a) A Type I
Consider the test of H0: The defendant is not guilty against Ha: The defendant is guilty.a. Explain, in context, the conclusion of the test if H0 is rejected.b. Describe, in context, a Type I
Consider the test of H0: The new drug is safe against Ha: the new drug is not safe.a. Explain, in context, the conclusion of the test if H0 is rejected.b. Describe, in context, a Type I error.c.
A marketing study conducts 60 significance tests about means and proportions for several groups. Of them, 3 tests are statistically significant at the 0.05 level. The study’s final report stresses
For testing H0: p = 1/3 (astrologers randomly guessing) against Ha: p > 1/3 with n = 116, Example 12 showed that P(Type II error) = 0.02 when p = 0.50. Now suppose that p = 0.35. Recall that
Consider Example 13 about the power of the test of H0: p = 0.1 against Ha: p > 0.1 used to test the effectiveness of a manual therapy in opening blocked tubes, where p is the probability of at
Refer to the web app from Activity 2 at the end of this section, now assuming that we are using the two-sided test H0: p = 0.33 against Ha: p ≠ 0.33. (Select “not equal” for the type of the
When the 2010 General Social Survey asked, €œWould you be willing to pay much higher taxes in order to protect the environment?€ (variable GRNTAXES), 459 people answered yes and
An Associated Press article appearing in the New York Times in March 2015 mentioned that “In the late 1980s, support for gay marriage was essentially unheard of in America. Just a quarter century
Is the ideal number of children equal or different from 2? For testing that the mean response from the 2014 GSS equals 2.0 for the question, €œWhat do you think is the ideal number of
When all subjects in the 2012 GSS who were working full- or part-time were asked how many hours they worked in the previous week at all jobs (variable HRS1), software produced the following
Example 10 compared mean political beliefs (on a 1 to 7 point scale) to the moderate value of 4.0, using GSS data. Test whether the population mean equals 4.00 for females, for whom the sample mean
A crossover study on comparing a magnetic device to placebo for reducing pain in 54 people suffering from low back or knee pain (neuromagnetics.mc.vanderbilt.edu/publications) reported a significant
What is wrong with expressing hypotheses about proportions and means in a form such as H0: p̂ = 0.50 and H0: x̅ = 0?
The P-value for testing H0: μ = 100 against Ha: μ ≠ 100 is 0.001. This indicates thata. There is strong evidence that μ = 100.b. There is strong evidence that μ ≠ 100, since if μ were equal
When H0 is true in a t test with significance level 0.05, the probability that the P-value falls ≤ 0.05a. Equals 0.05.b. Equals 0.95.c. Equals 0.05 for a one-sided test and 0.10 for a two sided
Exercise 9.34 concerned an industrial plant that may be exceeding pollution limits. An environmental action group took four readings to analyze whether the true mean discharge of wastewater per hour
For a test of H0: μ = 0 against Ha: μ > 0 based on n = 30 observations and using a = 0.05 significance level, P(Type II error) = 0.36 at μ = 4. Identify the response that is incorrect.a. At μ
True or False. If we reject H0: μ = 0 in a study about change in weight on a new diet using α = 0.01, then we also reject it using α = 0.05.
True or False. A 95% confidence interval for μ = population mean IQ is (96, 110). So, in the test of H0: μ = 100 against Ha: μ ≠ 100, the P-value > 0.05.
For a fixed significance level a, the probability of a Type II error increases when the sample size increases.
When testing H0: μ = 100 against Ha: μ ≠ 100, the probability of a Type II error decreases the further the true population mean m is from 100.
The P-value is the probability that H0 is true.
According to the Bureau of Labor Statistics, the official unemployment rate was 10.4% among blacks and 4.7% among whites as of February 2015. (www.bls.gov/).a. Identify the response variable and the
The 2011 Bedroom Sleep poll of a random sample of 1500 adults reported that respondents slept an average of 6.5 hours on weekdays and 7.2 hours on weekends, and that 21% of respondents got eight or
A National Center for Health Statistics data brief published in 2015 (Nr. 181) looked at the association between lung obstruction and smoking status in adults 40 to 79 years old. In a random sample
To increase Barack Obama€™s visibility and to raise money for the campaign leading up to the 2008 presidential election, Obama€™s analytics team conducted an A/B test with his

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