Describe a circumstance in which stratified sampling would be an appropriate sampling method.
> If we reject the null hypothesis when the statement in the null hypothesis is true, we have made a Type_____ error.
> _______ is a procedure, based on sample evidence and probability, used to test statements regarding a characteristic of one or more populations.
> (a) A_______ is a statement regarding a characteristic of one or more populations. (b) The________ is a statement of no change, no effect, or no difference. (c) The_______ is a statement we are trying to find evidence to support.
> In your own words, explain the difference between “beyond all reasonable doubt” and “beyond all doubt.” Use these phrases to explain why we never “accept” the statement in the null hypothesis.
> A retail store manager wants to conduct a study regarding the shopping habits of his customers. He selects the first 60 customers who enter his store on a Saturday morning.
> The following is a quotation from Sir Ronald A. Fisher, a famous statistician. For the logical fallacy of believing that a hypothesis has been proved true, merely because it is not contradicted by the available facts, has no more right to insinuate itsel
> What happens to the probability of making a Type II error, b, as the level of significance ,, decreases? Why?
> If the consequences of making a Type I error are severe, would you choose the level of significance, , to equal 0.01, 0.05, or 0.10? Why?
> Designed by Bill Bengen, the 4 percent rule says that a retiree may withdraw 4% of savings during the first year of retirement, and then each year after that withdraw the same amount plus an adjustment for inflation. Under this rule, your retirement savi
> Refer to Problem 16. Researchers must choose the level of significance based on the consequences of making a Type I error. In your opinion, is a Type I error or Type II error more serious? Why? On the basis of your answer, decide on a level of significan
> The manufacturer of Prolong Engine Treatment claims that if you add one 12-ounce bottle of its $20 product, your engine will be protected from excessive wear. An infomercial claims that a woman drove 4 hours without oil, thanks to Prolong. Consumer Repor
> According to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the fre
> According to the Centers for Disease Control and Prevention, 20.8% of high school students currently use electronic cigarettes. A high school counselor is concerned the use of e-cigs at her school is higher. (a) Determine the null and alternative hypothe
> According to popcorn.org, the mean consumption of popcorn annually by Americans is 54 quarts. The marketing division of popcorn.org unleashes an aggressive campaign designed to get Americans to consume even more popcorn. (a) Determine the null and a
> A can of soda is labeled as containing 12 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. (a) Determine the null and alternative hypotheses that would be used to deter
> A(n)_____sample is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
> Assessed value of a house
> For the hypotheses in Problem 16, the null hypothesis is not rejected.
> For the hypotheses in Problem 15, the null hypothesis is rejected.
> For the hypotheses in Problem 14, the null hypothesis is rejected.
> For the hypotheses in Problem 13, the null hypothesis is not rejected.
> For the hypotheses in Problem 20, the null hypothesis is not rejected.
> For the hypotheses in Problem 19, the null hypothesis is rejected.
> For the hypotheses in Problem 18, the null hypothesis is not rejected.
> For the hypotheses in Problem 17, the null hypothesis is not rejected.
> For the hypotheses in Problem 16, the null hypothesis is rejected.
> For the hypotheses in Problem 15, the null hypothesis is not rejected.
> Why are convenience samples ill advised?
> For the hypotheses in Problem 14, the null hypothesis is not rejected.
> For the hypotheses in Problem 13, the null hypothesis is rejected.
> In 2017, the standard deviation of SAT score on the Evidence-based Reading and Writing Test for all students taking the exam was 100. A teacher believes that, due to changes to high school curricula, the standard deviation of SAT score has decreased.
> According to the CTIA–The Wireless Association, the mean monthly revenue per cell phone was $38.66 in 2017. A researcher suspects the mean monthly revenue per cell phone is different today.
> According to the Centers for Disease Control and Prevention, 19.6% of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6- to 11-year-olds who are overweight is different in her school district.
> The standard deviation in the pressure required to open a certain valve is known to be = 0.7 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure variability has been reduced.
> Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least 32 ounces. A consumer advocate feels that a certain peanut butter manufacturer is shorting customers by underfilling the jars.
> According to the National Association of Home Builders, the mean price of an existing single-family home in 2018 was $395,000. A real estate broker believes that existing home prices in her neighborhood are lower.
> Historically, the time to order and deliver a pizza at Jimbo’s pizza was 48 minutes. Jim, the owner, implements a new system for ordering and delivering pizzas that he believes will reduce the time required to get a pizza to his customers.
> H0: = 7.8 H1: ≠ 7.8
> Which sampling method does not require a frame?
> H0: = 120 H1: < 120
> H0: p = 0.76 H1: p > 0.76
> H0: = 4.2 H1: ≠ 4.2
> H0: p = 0.2 H1: p < 0.2
> H0: = 5 H1: > 5
> True or False: Sample evidence can prove a null hypothesis is true.
> The______ is the probability of making a Type I error.
> If we do not reject the null hypothesis when the statement in the alternative hypothesis is true, we have made a Type____ error.
> What requirements must be satisfied in order to construct a confidence interval about a population proportion?
> For what type of variable does it makes sense to construct a confidence interval about a population mean?
> For what type of variable does it make sense to construct a confidence interval about a population proportion?
> Does chewing your food for a longer period of time reduce one’s caloric intake of food at dinner? A researcher requires a sample of 75 healthy males to chew their food twice as long as they normally do. The researcher then records the calorie consumption
> A researcher wanted to know whether consumption of green tea on a daily basis reduces LDL (bad) cholesterol. She obtains a random sample of 500 subjects. Each subject consumes at least 1 cup of green tea daily for 1 year. After 1 year, the researcher det
> Researchers at the Gallup Organization asked a random sample of 1016 adult Americans aged 21 years or older, “Right now, do you think the state of moral values in the country as a whole is getting better, or getting worse?”
> A developmental mathematics instructor wishes to estimate the typical amount of time students dedicate to studying mathematics in a week. She asks a random sample of 50 students enrolled in developmental mathematics at her school to report the amount of
> Researchers conducted a study to see the effect of specific lifestyle and dietary changes for preventing long-term weight gain. The study involved the consolidation of three cohorts from the Nurses’ Health Study (NHS): (1) cohort of 121,701 female regist
> Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_4_21. The data represent the status of licenses for short-term rentals in New Orleans, where “Yes” indicates the license is expired and “No” indicates the license is not expired. Sour
> The following data represent the property tax for a random sample of 50 single-family homes in the city of Houston. Suppose you want to estimate the typical property real estate tax for a single-family home in the city of Houston. (a) What type of variab
> Sleep apnea is a disorder in which you have one or more pauses in breathing or shallow breaths while you sleep. In a cross-sectional study of 320 individuals who suffer from sleep apnea, it was found that 192 had gum disease. Note: In the general populat
> Harris Interactive conducted a poll of a random sample of 2234 adult Americans 18 years of age or older and asked, “Which is more annoying to you, tailgaters or slow drivers who stay in the passing lane?” Among those surveyed, 1184 were more annoyed by t
> Research the sampling methods used by a market research firm in your neighborhood. Report your findings to the class. The report should include the types of sampling methods used, number of stages, and sample size.
> Clayton Kershaw of the Los Angeles Dodgers is one of the premier pitchers in baseball. His most popular pitch is a four-seam fastball. The data below represent the pitch speed (in miles per hour) for a random sample of 18 of his four-seam fastball pitche
> In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard deviation of $15. Construct and interpret a 99% confidence
> In a survey of 1008 adult Americans, the Gallup organization asked, “When you retire, do you think you will have enough money to live comfortably or not?” Of the 1008 surveyed, 526 stated that they were worried about having enough money to live comfortab
> Fifty rounds of a new type of ammunition were fired from a test weapon, and the muzzle velocity of the projectile was measured. The sample had a mean muzzle velocity of 863 meters per second and a standard deviation of 2.7 meters per second. Construct an
> In a random sample of 100 estate tax returns that was audited by the Internal Revenue Service, it was determined that the mean amount of additional tax owed was $3421 with a standard deviation of $2583. Construct and interpret a 90% confidence interval f
> Based on a poll conducted by the Centers for Disease Control, 862 of 1013 randomly selected adults said that they always wear seat belts. Construct and interpret a 95% confidence interval for the proportion of adults who always wear seat belts.
> Self-driving vehicles periodically suffer from a disengagement of the self-driving feature. In these cases, it is important to know how long it takes for the driver to manually take control of the vehicle. In a study of 487 instances where a self-driving
> A simple random sample of size n = 210 is drawn from a population. The sample mean is found to be / = 20.1, and the sample standard deviation is found to be s = 3.2. Construct a 90% confidence interval for the population mean
> A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be / = 120.5, and the sample standard deviation is found to be s = 12.9. Construct a 99% confidence interval for the population mean.
> A simple random sample of size n = 17 is drawn from a population that is normally distributed. The sample mean is found to be / = 3.25, and the sample standard deviation is found to be s = 1.17. Construct a 95% confidence interval for the population mean
> Research the origins of the Gallup Poll and the current sampling method the organization uses. Report your findings to the class.
> A simple random sample of size n = 12 is drawn from a population that is normally distributed. The sample mean is found to be / = 45, and the sample standard deviation is found to be s = 14. Construct a 90% confidence interval for the population mean.
> A simple random sample of size n = 785 adults was asked if they follow college football. Of the 785 surveyed, 275 responded that they did follow college football. Construct a 95% confidence interval for the population proportion of adults who follow coll
> A simple random sample of size n = 300 individuals who are currently employed is asked if they work at home at least once per week. Of the 300 employed individuals surveyed, 35 responded that they did work at home at least once per week. Construct a 99%
> What requirements must be satisfied in order to construct a confidence interval about a population mean?
> Put the following in order from least to greatest. • t0.10 with 5 degrees of freedom • t0.10 with 15 degrees of freedom • z0.10
> State the properties of Student’s t-distribution.
> The notation ta is the t-value such that the area under the t-distribution to the right of ta is______ .
> As the number of degrees of freedom in the t-distribution increases, the spread of the distribution________ (increases/ decreases).
> Population A has standard deviation / and population B has standard deviation /How many times larger than Population A’s sample size does Population B’s need to be to estimate with the same margin of error? (Hint: Compute /
> Suppose you have two populations: Population A—All students at Illinois State University (N = 21,000) and Population B—All residents of the city of Homer Glen, IL (N = 21,000). You want to estimate the mean age of each population using two separate sampl
> What is random sampling? Why is it necessary for a sample to be obtained randomly rather than conveniently? Will randomness guarantee that a sample will provide accurate information about the population? Explain.
> The mean age of the 45 presidents of the United States (as of 2018) on the day of inauguration is 55.0 years, with a standard deviation of 6.6 years. A researcher constructed a 95% confidence interval for the mean age of presidents on inauguration day. H
> Explain what is meant by degrees of freedom.
> The procedure for constructing a t-interval is robust. Explain what this means.
> Explain why the t-distribution has less spread as the number of degrees of freedom increases.
> A question on the General Social Survey was, “When you drink, how many drinks do you have?” The survey was administered to a random sample of 243 adult Americans aged 21 or older. Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_2_4
> Researchers Havar Brendryen and Pal Kraft conducted a study in which 396 subjects were randomly assigned to either an experimental smoking cessation program or control group. The experimental program consisted of the Internet and phone-based Happy Ending
> The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can be modeled by the exponential distribution with = =
> IQ scores based on the Wechsler Intelligence Scale for Children (WISC) are known to be approximately normally distributed with = 100 and =15. (a) Use StatCrunch, Minitab, or some other statistical software to simulate obtaining 100 simple random sampl
> The following small data set represents a simple random sample from a population whose mean is 50. (a) A normal probability plot indicates that the data could come from a population that is normally distributed with no outliers. Compute a 95% confidence
> The data sets represent simple random samples from a population whose mean is 100. (a) Compute the sample mean of each data set. (b) For each data set, construct a 95% confidence interval about the population mean. (c) What effect does the sample size n
> Suppose a political strategist wants to get a sense of how American adults aged 18 years or older feel about health care and health insurance. (a) In a political poll, what would be a good frame to use for obtaining a sample? (b) Explain why simple rando
> A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours. (a) How many people are needed to estimate the
> A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books. (a) How many subjects are needed to estimate the number of books Americans read the previous yea
> Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males within 1.5 points with 90% confidence, assuming
> Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to 29-year-old females within 2 points with 99% confidence assumin
> The Sullivan Statistics Survey II asks, “What percent of one’s income should an individual pay in federal income taxes?” Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyII using the file format of your choice for th
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Compute the population mean length of a tornado in the United States in
> The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 6.16 represents 6,160,000 shares traded), represent the volume of PepsiCo stock traded for a random sample of 40 trading days in 2018. (a)
