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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

Figure 4.15 shows a randomization distribution for testing H0: p = 0.3 vs Ha: p < 0.3. In each case, use the distribution to decide which value is closer to the p-value for the observed sample
Figure 4.16 shows a randomization distribution for testing H0: Î¼1= Î¼2vs Ha: Î¼1‰ Î¼2. The statistic used for each sample is D =
xÌ…1=95.7, xÌ…2=93.5 or xÌ…1= 94.1, xÌ…2= 96.3Refer to Figure 4.16, which shows a randomization distribution for hypotheses H0 : Î¼1 =
Data 4.5 on page 228 discusses a test to determine if the mean level of arsenic in chicken meat is above 80 ppb. If a restaurant chain finds significant evidence that the mean arsenic level is above
It is believed that sunlight offers some protection against multiple sclerosis (MS) since the disease is rare near the equator and more prevalent at high latitudes. What is it about sunlight that
The data for the 10,000 simulated dog€“owner matches shown in Figure 4.7 on page 237 are given in Table 4.6. We are testing H0: p = 0.5 (random guessing) vs Ha: p > 0.5 (evidence of a
In Data 4.6 on page 240 we look at finger-tapping rates to see if ingesting caffeine increases average tap rate. Letting Î¼cand Î¼nrepresent the average tap rate of people
Exercise 4.38 on page 235 describes a study to investigate whether a recorded phone call is more effective than a flyer in persuading voters to vote for a particular candidate. The response variable
Exercise 4.37 on page 235 describes a study to investigate which method, a recorded phone call or a flyer, is more effective in persuading voters to vote for a particular candidate. Since in this
A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. A new study provides the best evidence yet that this test saves lives. The proportion of
An education study in Tennessee in the 1980s (known as Project Star) randomly assigned 12,000 students to kindergarten classes, with the result that all classes had fairly similar socioeconomic mixes
Data 4.2 on page 223 describes an experiment to study the effects of smiling on leniency in judging students accused of cheating. The full data are in Smiles. In Example 4.2 we consider hypotheses
Using the definition of a p-value, explain why the area in the tail of a randomization distribution is used to compute a p-value.
Two professors at the University of Arizona were interested in whether having students actually play a game would help them analyze theoretical properties of the game. The professors performed an
Exercise 4.62 describes an experiment involving playing games in class. One concern in the experiment is that the exam question related to Game 1 might be a lot easier or harder than the question for
How small would a p-value have to be in order for you to consider results statistically significant? Explain. (There is no correct answer! This is just asking for your personal opinion. We’ll study
Give a p-value. State the conclusion of the test based on this p-value in terms of ‘‘Reject H0” or ‘‘Do not reject H0” if we use a 5% significance level.p-value = 0.0007
Give a p-value. State the conclusion of the test based on this p-value in terms of ‘‘Reject H0” or ‘‘Do not reject H0” if we use a 5% significance level.p-value = 0.0320
Give a p-value. State the conclusion of the test based on this p-value in terms of ‘‘Reject H0” or ‘‘Do not reject H0” if we use a 5% significance level.p-value = 0.2531
Give a p-value. State the conclusion of the test based on this p-value in terms of ‘‘Reject H0” or ‘‘Do not reject H0” if we use a 5% significance level.p-value = 0.1145
Using the p-value given, are the results significant at a 10% level? At a 5% level? At a 1% level?p-value = 0.2800
Using the p-value given, are the results significant at a 10% level? At a 5% level? At a 1% level?p-value = 0.008
Using the p-value given, are the results significant at a 10% level? At a 5% level? At a 1% level?p-value = 0.0621
Match the four p-values with the appropriate conclusion:I. 0.0875II. 0.5457III. 0.0217IV. 0.00003(a) The evidence against the null hypothesis is significant, but only at the 10% level.(b) The
Match the four p-values with the appropriate conclusion:I. 0.00008II. 0.0571III. 0.0368IV. 0.1753(a) The evidence against the null hypothesis is significant, but only at the 10% level.(b) The
Test A is described in a journal article as being significant with ‘‘P < .01”; Test B in the same article is described as being significant with ‘‘P < .10.” Using only this
In each case, indicate whether the statement is a proper interpretation of what a p-value measures.(a) The probability the null hypothesis H0 is true.(b) The probability that the alternative
In Data 4.4 on page 227, we introduce the results of a May 2010 Gallup poll of 1029 U.S. adults. When asked if they view divorce as ‘‘morally acceptable,” 71% of the men and 67% of the women in
Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. A recent study investigates whether the same phenomenon holds true in primates. The grey mouse
Exercise 4.40 on page 236 describes an ongoing game of Euchre, in which the game continues until one of the two teams is deemed to be statistically significantly better than the other team. Which
The consumption of caffeine to benefit alertness is a common activity practiced by 90% of adults in North America. Often caffeine is used in order to replace the need for sleep. One recent study
How influenced are consumers by price and marketing? If something costs more, do our expectations lead us to believe it is better? Because expectations play such a large role in reality, can a
Figure 4.26 shows a scatterplot of the acidity (pH) for a sample of n = 53 Florida lakes vs the average mercury level (ppm) found in fish taken from each lake. The full dataset is introduced in Data
Suppose in a two-tailed test of H0: ρ = 0 vs Ha: ρ ≠ 0, we reject H0 when using a 5% significance level. Which of the conclusions below (if any) would also definitely be valid for the same data?
Exercise 4.62 describes a situation in which game theory students are randomly assigned to play either Game 1 or Game 2, and then are given an exam containing questions on both games. Two one-tailed
Use StatKey or other technology to create a randomization distribution for the paired data in the quiz€“lecture pulse test described in Exercise 4.141. Find the p-value for the original
Introductory statistics students fill out a survey on the first day of class. One of the questions asked is €˜€˜How many hours of exercise do you typically get each
Use StatKey or other technology and the data in Exercise Hours to carry out any two of the three randomization procedures as described in parts (a) to (c) in Exercise 4.144 comparing mean hours of
In Exercise 3.80 on page 203, we found a 95% confidence interval for the difference in proportion of rats showing compassion, using the proportion of female rats minus the proportion of male rats, to
The Auburn, Maine, school district conducted an early literacy experiment in the fall of 2011. In September, half of the kindergarten classes were randomly assigned iPads (the intervention group)
Newscientist.com ran the headline ‘‘Breakfast Cereals Boost Chances of Conceiving Boys,” based on an article which found that women who eat breakfast cereal before becoming pregnant are
Does heavy cell phone use affect brain activity? There is some concern about possible negative effects of radiofrequency signals delivered to the brain. In a randomized matched-pairs study, 47
In Exercise 4.16 on page 232, we describe an observational study investigating a possible relationship between exposure to organophosphate pesticides as measured in urinary metabolites (DAP) and
Diabetes tends to be more prevalent in urban populations, but why this is so is not fully understood. A recent study on mice was designed to investigate the link between diabetes and air pollution.
Does consuming beer attract mosquitoes? Exercise 4.17 on page 232 discusses an experiment done in Africa testing possible ways to reduce the spread of malaria by mosquitoes. In the experiment, 43
Exercise 4.19 on page 232 describes a study investigating the effects of exercise on cognitive function. Separate groups of mice were exposed to running wheels for 0, 2, 4, 7, or 10 days. Cognitive
Exercise 4.29 on page 234 describes a company that advertises that its milled flaxseed contains, on average, at least 3800 mg of ALNA, the primary omega-3 fatty acid in flaxseed, per tablespoon. In
Testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If it is found to be more effective, it will be prescribed to millions
Using your statistics class as a sample to see if there is evidence of a difference between male and female students in how many hours are spent watching television per week.Indicate whether it makes
Using a sample of 10 games each to see if your average score at Wii bowling is significantly more than your friend’s average score.Indicate whether it makes more sense to use a relatively large
Testing to see if a well-known company is lying in its advertising. If there is evidence that the company is lying, the Federal Trade Commission will file a lawsuit against them.Indicate whether it
Testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement.Indicate whether it makes more sense to use a
A pharmaceutical company is testing to see whether its new drug is significantly better than the existing drug on the market. It is more expensive than the existing drug. Which significance level
The situation described in Exercise 4.93Testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If it is found to be more
The situation described in Exercise 4.94Using your statistics class as a sample to see if there is evidence of a difference between male and female students in how many hours are
The situation described in Exercise 4.95Using a sample of 10 games each to see if your average score at Wii bowling is significantly more than your friend’s average score.Describe what it means in
The situation described in Exercise 4.96Testing to see if a well-known company is lying in its advertising. If there is evidence that the company is lying, the Federal Trade Commission will file a
(a) If we are conducting a statistical test and determine that our sample shows significant results, there are two possible realities: We are right in our conclusion or we are wrong. In each case,
The situation described in Exercise 4.97Testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
Null and alternative hypotheses for a test are given. Give the notation (x̅, for example) for a sample statistic we might record for each simulated sample to create the randomization
Null and alternative hypotheses for a test are given. Give the notation (x̅, for example) for a sample statistic we might record for each simulated sample to create the randomization
Null and alternative hypotheses for a test are given. Give the notation (x̅, for example) for a sample statistic we might record for each simulated sample to create the randomization
Exercise 4.38 on page 235 describes a possible study to see if there is evidence that a recorded phone call is more effective than a mailed flyer in getting voters to support a certain candidate. The
Null and alternative hypotheses for a test are given. Give the notation (x̅, for example) for a sample statistic we might record for each simulated sample to create the randomization
Null and alternative hypotheses for a test are given. Give the notation (x̅, for example) for a sample statistic we might record for each simulated sample to create the randomization
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
Give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey
In the 2010 World Cup, Paul the Octopus (in a German aquarium) became famous for being correct in all eight of the predictions it made, including predicting Spain over Germany in a semifinal match.
For the Paul the Octopus data in Exercise 4.123, use StatKey or other technology to create a randomization distribution. Calculate a p-value. How unlikely is his success rate if Paul the Octopus is
We flip a coin 150 times and get 90 heads, so the sample proportion of heads is p̂ = 90/150 = 0.6. To test whether this provides evidence that the coin is biased, we create a randomization
In Data 4.6 we look at finger-tapping rates to see if ingesting caffeine increases average tap rate. The sample data for the 20 subjects (10 randomly getting caffeine and 10 with no-caffeine) are
In Data A.1 on page 136, we introduce a study in which mice are randomly separated into one group on a normal light dark cycle and one group with bright light on all the time. Although the mice ate
Data 4.5 on page 228 introduces a situation in which a restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level
For the study in Exercise 4.128, use StatKey or other technology to create the randomization distribution for this test. Find the p-value and give a conclusion for the test. Should the restaurant
Exercise 4.82 on page 261 describes a study in which a sample of 24 adults are randomly divided equally into two groups and given a list of 24 words to memorize. During a break, one group takes a
Scientists studying lion attacks on humans in Tanzania found that 95 lion attacks happened between 6 pm and 10 pm within either five days before a full moon or five days after a full moon. Of these,
After exercise, massage is often used to relieve pain, and a recent study shows that it also may relieve inflammation and help muscles heal. In the study, 11 male participants who had just
Data 4.3 on page 224 describes a study of a possible relationship between the perceived malevolence of a team€™s uniforms and penalties called against the team. In Example 4.31 on page 270
Exercise 2.23 on page 57 introduces a study in which 40 participants are trained to solve problems in a certain way and then asked to solve an unfamiliar problem that requires fresh insight. Half of
In 1980, the active ingredient in marijuana was shown to outperform a placebo in reducing nausea in chemotherapy patients, with a p-value of 0.0004. Many studies are now underway to see if the drug
For the study in Exercise 4.135, use StatKey or other technology to create the randomization distribution for this data. Use the distribution to calculate a p-value for the test, and compare this
In October before the 2008 US presidential election, ABC News and the Washington Post jointly conducted a poll of ‘‘a random national sample” and asked people who they intended to vote for in
Use StatKey or other technology to create a randomization distribution for the poll described in Exercise 4.137. What is the p-value for the test? Would this have been convincing evidence that Obama
In this exercise, we see that it is possible to use counts instead of proportions in testing a categorical variable. Data 4.7 describes an experiment to investigate the effectiveness of the two drugs
(a) For the study in Exercise 4.139, use StatKey or other technology to create a randomization distribution for these data. Use the distribution to calculate a p-value. Interpret the results.(b) In
Do you think that students undergo physiological changes when in potentially stressful situations such as taking a quiz or exam? A sample of statistics students were interrupted in the middle of a
A statistics instructor would like to ask ‘‘clicker” questions that about 80% of her students in a large lecture class will get correct. A higher proportion would be too easy and a lower
Hypotheses: H0: μ = 15 vs Ha: μ ≠ 15(a) 95% confidence interval for μ: 13.9 to 16.2(b) 95% confidence interval for μ: 12.7 to 14.8(c) 90% confidence
Hypotheses: H0: p = 0.5 vs Ha: p ≠ 0.5(a) 95% confidence interval for p: 0.53 to 0.57(b) 95% confidence interval for p: 0.41 to 0.52(c) 99% confidence interval for p: 0.35 to 0.55Hypotheses for a
Hypotheses: H0: ρ = 0 vs Ha: ρ ≠ 0. In addition, in each case for which the results are significant, give the sign of the correlation.(a) 95% confidence interval for ρ: 0.07 to 0.15(b) 90%
Hypotheses: H0: μ1 = μ2 vs Ha: μ1 ≠ μ2. In addition, in each case for which the results are significant, state which group (1 or 2) has the larger mean.(a) 95% confidence interval for μ1 −

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