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mathematics
elementary statistics picturing

Questions and Answers of Elementary Statistics Picturing

Polling organizations typically generate the last digits of telephone numbers so that people with unlisted numbers are included. Listed below are digits randomly generated by STATDISK. Such generated
Listed below are 12 lengths (in minutes) of randomly selected movies from Data Set 9 in Appendix B.a. Construct a 99% confidence interval estimate of the mean length of all movies.b. Assuming that it
Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below (based on data from “Content and Ratings of Teen-Rated Video
Margin of error: three percentage points; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 87%.Use the given data to find the minimum sample size required to
The Genetics and IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 574 babies were born to parents using the
Refer to Data Set 9 from Appendix B and construct a 95% confidence interval estimate of the mean gross amount for the population of all movies. Assume that the population standard deviation is known
Refer to Data Set 24 in Appendix B and construct the 99% confidence interval estimate of the mean FICO score for the population. Assume that the population standard deviation is 92.2. Data Set 24:
Listed below are the ages of the Presidents of the United States at the times of their inaugurations. Construct a 99% confidence interval estimate of the mean age of presidents at the times of their
An interesting and popular hypothesis is that individuals can temporarily postpone their death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, it was
What sample size is needed to estimate the mean white blood cell count (in cells per microliter) for the population of adults in the United States? Assume that you want 99% confidence that the sample
A physician wants to develop criteria for determining whether a patient?s pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Use
An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is
You want to estimate the mean weight loss of people one year after using the Atkins weight loss program. How many people on that program must be surveyed if we want to be 95% confident that the
Figure 7-6 and Table 7-1 summarize the decisions made when choosing between the normal and t distributions. An alternative method included in some textbooks (but almost never used by professional
In a survey of 1002 people, 701 said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.a.
You want to estimate the mean amount of annual tuition being paid by current full-time college students in the United States. First use the range rule of thumb to make a rough estimate of the
A study of 420,095 Danish cell phone users found that 135 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be
In a Pew Research Center poll, 73% of 3011 adults surveyed said that they use the Internet. Construct a 95% confidence interval estimate of the proportion of all adults who use the Internet. Is it
The methods of this section assume that sampling is from a population that is very large or infinite, and that we are sampling with replacement. If we have a relatively small population and sample
In an Accountemps survey of 150 senior executives, 47% said that the most common job interview mistake is to have little or no knowledge of the company. Construct a 99% confidence interval estimate
After 276 passengers on the Queen Elizabeth II cruise ship contracted a norovirus, America Online presented this question on its Internet site: “Would the recent outbreak deter you from taking a
As the newly hired manager of a company that provides cell phone service, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line
The use of the Internet is constantly growing. How many randomly selected adults must be surveyed to estimate the percentage of adults in the United States who now use the Internet? Assume that we
A campaign was designed to convince car owners that they should fill their tires with nitrogen instead of air. At a cost of about $5 per tire, nitrogen supposedly has the advantage of leaking at a
As this book was being written, former New York City mayor Rudolph Giuliani announced that he was a candidate for the presidency of the United States. If you are a campaign worker and need to
Refer to Data Set 18 in Appendix B and find the sample proportion of M&Ms that are green. Use that result to construct a 95% confidence interval estimate of the population percentage of M&Ms
Refer to Data Set 3 in Appendix B. a. Based on the sample results, find the best point estimate of the percentage of college students who gain weight in their freshman year. b. Construct a 95%
Refer to Data Set 14 in Appendix B, and consider days with precipitation values different from 0 to be days with precipitation. Construct a 95% confidence interval estimate of the proportion of
Refer to Data Set 9 in Appendix B and find the proportion of movies with R ratings. Use that proportion to construct a 95% confidence interval estimate of the proportion of all movies with R ratings.
Assume that a coin is modified so that it favors heads, and 100 tosses result in 95 heads. Find the 99% confidence interval estimate of the proportion of heads that will occur with this coin. What is
Suppose n trials of a binomial experiment result in no successes. According to the Rule of Three, we have 95% confidence that the true population proportion has an upper bound of 3/n. (See “A Look
A New York Times article about poll results states, “In theory, in 19 cases out of 20, the results from such a poll should differ by no more than one percentage point in either direction from what
Using 52 rainfall amounts for Sundays in Boston, a test of the claim that μ > 0 in. results in a P-value of 0.0091. What does the P-value suggest about the claim? In general, what does the
A simple random sample of 1088 adults between the ages of 18 and 44 is conducted. It is found that 261 of the 1088 adults smoke (based on data from the National Health Interview Survey). Use a 0.05
Listed below are the winning times (in seconds) of women in the 100-meter dash for consecutive summer Olympic games, listed in order by year. Assume that the times are sample data from a larger
In reporting on an Elle MSNBC.COM survey of 61,647 people, Elle magazine stated that “just 20% of bosses are good communicators.” Without performing formal calculations, do the sample results
In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses, 1261 answered “no,” 491 answered “yes,” and 384 had no opinion. What is the sample
Data Set 4 in Appendix B lists the amounts of nicotine (in milligrams per cigarette) in 25 different king size cigarettes. If we want to use that sample to test the claim that all king size
Given a simple random sample of 20 speeds of cars on Highway 405 in California, you want to test the claim that the sample values are from a population with a mean greater than the posted speed limit
Hypothesis tests of claims about the population mean or population standard deviation both require a simple random sample from a normally distributed population. How does the normality requirement
A very large simple random sample consists of the differences between the heights of the first-born male child and the second-born male child. With n = 295,362 x = 0.019 in., and s = 3.91 in., a test
A simple random sample is conducted of 1486 college students who are seeking bachelor’s degrees, and it includes 802 who earned bachelor’s degrees within five years. Use a 0.01 significance level
Exercise 1 lists the winning times (in seconds) of women in the 100-meter dash for consecutive summer Olympic games.a. What is the level of measurement of the data? (nominal, ordinal, interval,
America Online conducted a survey in which Internet users were asked to respond to this question: Do you want to live to be 100?” Among 5266 responses, 3042 were responses of “yes.” Is it valid
Because the amounts of nicotine in king size cigarettes listed in Data Set 4 in Appendix B constitute a sample of size n = 25, we must satisfy the requirement that the population is normally
In statistics, what does df denote? If a simple random sample of 20 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean
There is a claim that the lengths of men’s hands have a standard deviation less than 200 mm. You plan to test that claim with a 0.01 significance level by constructing a confidence interval. What
Some magazines and newspapers conduct polls in which the sample results are a voluntary response sample. What is a voluntary response sample? In general, can such a voluntary response sample be used
When planning for construction of a parkway, engineers must consider the weights of cars to be sure that the road surface is strong enough. A simple random sample of 32 cars yields a mean of 3605.3
Bottles of Bayer aspirin are labeled with a statement that the tablets each contain 325 mg of aspirin. A quality control manager claims that a large sample of data can be used to support the claim
In 280 trials with professional touch therapists, correct responses to a question were obtained 123 times. The P-value of 0.979 is obtained when testing the claim that p > 0.5 (the proportion of
If you want to construct a confidence interval to be used for testing the claim that college students have a mean IQ score that is greater than 100, and you want the test conducted with a 0.01
What is a t test? Why is the letter t used?
There is a claim that daily rainfall amounts in Boston have a standard deviation equal to 0.25 in. Sample data show that daily rainfall amounts are from a population with a distribution that is very
What does it mean when we say that a particular method of hypothesis testing is robust against departures from normality? Is the t test of a population mean robust against departures from normality?
Repeat Exercise 3 by assuming that weights of cars have a standard deviation known to be 520 lb. Repeat Exercise 3 When planning for construction of a parkway, engineers must consider the weights of
Use the sample values given in Exercise 1 to test the claim that the mean winning time is less than 11 sec. Use a 0.05 significance level. What can we conclude about winning times in the future?11.07
In preliminary results from couples using the Gender Choice method of gender selection to increase the likelihood of having a baby girl, 20 couples used the Gender Choice method with the result that
A hypothesis test that the Zone diet is effective (when used for one year) results in this conclusion: There is sufficient evidence to support the claim that the mean weight change is less than 0 (so
Unlike the preceding section, this section does not include a requirement that the value of the population standard deviation must be known. Which section is more likely to apply in realistic
There is a claim that men have foot breadths with a variance equal to 36 mm2. Is a hypothesis test of the claim that the variance is equal to 36 mm2 equivalent to a test of the claim that the
Among 30,617 randomly selected adults, 5787 consumed herbs within the past 12 months (based on data from “Use of Herbs Among Adults Based on Evidence-Based Indications: Findings From the National
Minitab is used to construct a histogram of the weights of a simple random sample of M&M candies, and the result is shown on the next page. a. Does the sample appear to be from a population with
Claim: A coin favors heads when tossed, and there are 90 heads in 100 tosses.Make a decision about the given claim. Use only the rare event rule stated in Section 8-2, and make subjective estimates
A recent study showed that 53% of college applications were submitted online (based on data from the National Association of College Admissions Counseling). Assume that this result is based on a
A jewelry designer claims that women have wrist breadths with a mean equal to 5 cm. A simple random sample of the wrist breadths of 40 women has a mean of 5.07 cm (based on Data Set 1 in Appendix B).
Claim about IQ scores of statistics instructors: μ > 100. Sample data: n = 15, x = 118, s = 11. The sample data appear to come from a normally distributed population with unknown μ and
Find the test statistic and critical value(s). Also, use Table A-4 to find limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative
An axial load of an aluminum can is the maximum weight that the sides can support before collapsing. The axial load is an important measure, because the top lids are pressed onto the sides with
Minitab is used to generate a histogram of the outcomes from 100 rolls of a die. What is wrong with the graph? MINITAB Frequency 22- 18- 16- L 14- 20- 12- 10 T N to Outcome -5 л- 9_
Claim: The proportion of households with telephones is greater than the proportion of 0.35 found in the year 1920. A recent simple random sample of 2480 households results in a proportion of 0.955
In a survey, 1864 out of 2246 randomly selected adults in the United States said that texting while driving should be illegal (based on data from Zogby International). Consider a hypothesis test that
The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(74, 12.5, 100) generates 100 values from a normally distributed
Refer to the histogram provided for Exercise 6 and construct the frequency distribution that summarizes the outcomes. Then find the mean of the 100 outcomes.
Claim: The mean pulse rate (in beats per minute) of students of the author is less than 75. A simple random sample of students has a mean pulse rate of 74.4.Make a decision about the given claim. Use
In a survey, 1640 out of 2246 randomly selected adults in the United States said that they use cell phones while driving (based on data from Zogby International). When testing the claim that the
In the manual “How to Have a Number One the Easy Way,” by KLF Publications, it is stated that a song “must be no longer than three minutes and thirty seconds” (or 210 seconds). A simple
Claim about daily rainfall amounts in Boston: μ < 0.20 in. Sample data: n = 19. x = 0.10 in, s = 0.26. The sample data appear to come from a population with a distribution that is very far from
Find the test statistic and critical value(s). Also, use Table A-4 to find limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative
Repeat Exercise 7 without making the assumption that the population standard deviation is known.Repeat Exercise 7The TI-83/84 Plus calculator can be used to generate random data from a normally
A hypothesis test is conducted with a 0.05 significance level, so that there is a 0.05 probability of making the mistake of rejecting a true null hypothesis. If two different independent hypothesis
Claim: Movie patrons have IQ scores with a standard deviation that is less than the standard deviation of 15 for the general population. A simple random sample of 40 movie patrons results in IQ
A survey of 750 people aged 14 or older showed that 35 of them were arrested within the last year (based on FBI data). Minitab was used to test the claim that fewer than 5% of people aged 14 or older
Claim about daily rainfall amounts in Boston: μ < 0.20 in. Sample data: n = 52, x = 0.10 in, s = 0.26 in. The sample data appear to come from a population with a distribution that is very far
Find the test statistic and critical value(s). Also, use Table A-4 to find limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative
The examples in this section involved the claim that post-1983 pennies have weights with a standard deviation less than 0.0230 g. Data Set 20 in Appendix B includes the weights of a simple random
Use the sample results from Exercise 7 to test the claim that the generated values are from a population with a standard deviation equal to 12.5. Use a 0.05 significance level.Exercise 7The TI-83/84
When designing a movie theater with stadium seating, engineers decide to consider the sitting eye heights of women. Those heights have a mean of 739 mm and a standard deviation of 33 mm and they are
The mean annual income of employees who took a statistics course is greater than $60,000.Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in symbolic
In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of
A simple random sample of the weights of 19 green M&Ms has a mean of 0.8635 g (as in Data Set 18 in Appendix B). Assume that ? is known to be 0.0565 g. Use a 0.05 significance level to test the
The proportion of people aged 18 to 25 who currently use illicit drugs is equal to 0.20 (or 20%).Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in
Two-tailed test with n = 15 and test statistic t = 1.495. Either use technology to find the P-value or use Table A-3 to find a range of values for the P-value. TABLE A-3 t Distribution: Critical t
The standard deviation of human body temperatures is equal to 0.62°F.Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in symbolic form. Be sure to use
The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds. In the first U.S. Open that used the Hawk-Eye system,
Two-tailed test with n = 9 and test statistic t = - 1.905. Either use technology to find the P-value or use Table A-3 to find a range of values for the P-value. TABLE A-3 t Distribution: Critical t
When 40 people used the Weight Watchers diet for one year, their weight losses had a standard deviation of 4.9 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone
The majority of college students have credit cards.Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in symbolic form. Be sure to use the correct symbol
When a fair die is rolled many times, the outcomes of 1, 2, 3, 4, 5, and 6 are equally likely, so the mean of the outcomes should be 3.5. The author drilled holes into a die and loaded it by
Test a claim about the mean body temperature of healthy adults: Left-tailed test with n = 11 and test statistic t = - 3.518. Either use technology to find the P-value or use Table A-3 to find a range

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