The village of Oak Lawn wishes to conduct a study regarding the income level of households within the village. The village manager selects 10 homes in the southwest corner of the village and sends an interviewer to the homes to determine household income.
> To test / a simple random sample of size n = 35 is obtained. (a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why? (b) If / = 101.9 and s = 5.9, compute the test statistic. (c
> To test /a simple random sample of size n = 13 is obtained from a population that is known to be normally distributed. (a) If / = 4.9 and s = 1.3, compute the test statistic. (b) Draw a t-distribution with the area that represents the P-value shaded. (c)
> To test / a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed. (a) If / = 18.3 and s = 4.3, compute the test statistic. (b) Draw a t-distribution with the area that represents the P-value shaded. (
> To test /a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed. (a) If /= 76.9 and s = 8.5, compute the test statistic. (b) If the researcher decides to test this hypothesis at the = 0.02 level of
> True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.
> Cold Stone Creamery is considering opening a new store in O’Fallon. Before opening, the company wants to know the percentage of households in O’Fallon that regularly visit an ice cream shop. The market researcher obtains a list of households in O’Fallon,
> When observed results are unlikely under the assumption that the null hypothesis is true, we say the result is_____ and we reject the null hypothesis.
> Explain what “statistical significance” means.
> The headline reporting the results of a poll conducted by the Gallup organization stated “Majority of Americans at Personal Best in the Morning.” The results indicated that a survey of 1100 Americans resulted in 55% stating they were at their personal be
> Discuss the advantages and disadvantages of using the Classical Approach to hypothesis testing. Discuss the advantages and disadvantages of using the P-value approach to hypothesis testing.
> Suppose we are testing the hypothesis / versus / and we find the P-value to be 0.02. Explain what this means. Would you reject the null hypothesis? Why?
> Suppose we are testing the hypothesis / versus / and we find the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?
> Explain what a P-value is. What is the criterion for rejecting the null hypothesis using the P-value approach?
> Yale University graduate student J. Kiley Hamlin conducted an experiment in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the
> Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease i
> Parapsychology (psi) is a field of study that deals with clairvoyance or precognition. Psi made its way back into the news when a professional, refereed journal published an article by Cornell psychologist Daryl Bem, in which he claimed to demonstrate th
> A polling organization conducts a study to estimate the percentage of households that speaks a foreign language as the primary language. It mails a questionnaire to 1023 randomly selected households throughout the United States and asks the head of house
> Simulate drawing 100 simple random samples of size n = 40 from a population whose proportion is 0.3. (a) Test the null hypothesis / each simulated sample. (b) If we test the hypothesis at the a = 0.1 level of significance, how many of the 100 samples wou
> Suppose you wish to find out the answer to the age-old question, “Do Americans prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to di
> In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans. (a) Consider the hypotheses /Explain what the researcher would be testing
> For every NFL game, there is a team that is expected to win by a certain number of points. In betting parlance, this is called the spread. For example, if the Chicago Bears are expected to beat the Green Bay Packers by three points, a sports bettor would
> The Sullivan Statistics Survey II asked, “Do you believe there is an income inequality discrepancy between males and females when each has the same experience and education?” Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanSta
> 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) Since 1950, the proportion of tornadoes that have been F0 is 0.465. The
> A headline read, “More Than Half of Americans Say Federal Taxes Too High.” The headline was based on a random sample of 1026 adult Americans in which 534 stated the amount of federal tax they have to pay is too high. Is this an accurate headline? Source:
> From Super Bowl I (1967) through Super Bowl XXXI (1997), the stock market increased if an NFL team won the Super Bowl and decreased if an AFL team won. This condition held 28 out of 31 years. (a) Suppose the likelihood of predicting the direction of the
> In 1997, 4% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 4% today. She randomly selects 120 pregnant mothers and finds that 3 of the
> Professors Honey Kirk and Diane Lerma of Palo Alto College developed a “learning community curriculum that blended the developmental mathematics and the reading curriculum with a structured emphasis on study skills.” In a typical developmental mathematic
> Suppose you are conducting a survey regarding the sleeping habits of students. From a list of registered students, you obtain a simple random sample of 150 students. One survey question is “How much sleep do you get?”
> Researchers looked at studies that were reported in newspapers with the goal of determining whether initial studies had results that could be reproduced. Reproducibility of results means that subsequent analysis confirms the conclusion of the original st
> When the area of the brain responsible for vision is destroyed, individuals experience cortical blindness. Patients with cortical blindness are unaware of any visual stimulus, including light. In a 52-year-old male patient with cortical blindness (as a r
> In an American Animal Hospital Association survey, 37% of respondents stated that they talk to their pets on the telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to t
> According to QSR Magazine, Chick-fil-A has the best accuracy of drive thru orders with 96.4% of all its drive thru orders filled correctly. The manager of a competing fast food restaurant wants to advertise that her drive thru is more accurate than C
> According to menstuff.org, 22% of married men have “strayed” at least once during their married lives. (a) Describe how you might go about administering a survey to assess the accuracy of this statement. (b) A survey of 500 married men indicated that 122
> In August 2002, 47% of parents with children in grades K–12 were satisfied with the quality of education the students receive. A recent Gallup poll found that 437 of 1013 parents with children in grades K–12 were satisfied with the quality of education t
> In 2000, 58% of females aged 15 and older lived alone, according to the U.S. Census Bureau. A sociologist tests whether this percentage is different today by obtaining a random sample of 500 females aged 15 and older and finds that 285 are living alone.
> In 1994, 52% of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents with children in high school felt it was a serious p
> In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together se
> According to the National Highway and Traffic Safety Administration, the proportion of fatal traffic accidents in the United States in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 105 traffic fatal
> An antigun advocate wants to estimate the percentage of people who favor stricter gun laws. He conducts a nationwide survey of 1203 randomly selected adults 18 years old and older. The interviewer asks the respondents, “Do you favor harsher penalties for
> Nexium is a drug that can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of Nexium claims that more than 94% of patients taking Nexium are healed within 8 weeks. In clinical trials, 2
> The drug Lipitor is meant to reduce cholesterol and LDL cholesterol. In clinical trials, 19 out of 863 patients taking 10 mg of Lipitor daily complained of flulike symptoms. Suppose that it is known that 1.9% of patients taking competing drugs complain o
> In his book, The Signal and the Noise, Nate Silver analyzed 733 predictions made by experts regarding political events. Of the 733 predictions, 338 were mostly true. (a) Determine the sample proportion of political predictions that were mostly true. (b)
> The website pundittracker.com keeps track of predictions made by individuals in finance, politics, sports, and entertainment. Jim Cramer is a famous TV financial personality and author. Pundittracker monitored 678 of his stock predictions (such as a reco
> Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individ
> Throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 100 companies to invest in. After 1 year, 53 of the companies wer
> H0: p = 0.4 versus H1: p ≠ 0.4 n = 1000; x = 420; a = 0.01
> H0: p = 0.9 versus H1: p ≠ 0.9 n = 500; x = 440; a = 0.05
> H0: p = 0.25 versus H1: p < 0.25 n = 400; x = 96; a = 0.1
> H0: p = 0.55 versus H1: p < 0.55 n = 150; x = 78; a = 0.1
> H0: p = 0.6 versus H1: p < 0.6 n = 250; x = 124; a = 0.01
> H0: p = 0.3 versus H1: p > 0.3 n = 200; x = 75; a = 0.05
> Determine the critical value for a two-tailed test regarding a population proportion at the = 0.05 level of significance.
> Determine the critical value for a left-tailed test regarding a population proportion at the = 0.1 level of significance.
> Determine the critical value for a right-tailed test regarding a population proportion at the = 0.01 level of significance
> Put the following P-values in order from weakest to strongest in terms of evidence against the statement in the null hypothesis. (a) 0.139 (b) 0.083 (c) 0.091 (d) 0.005 (e) 0.019
> 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.
