chapter 11 stats
Last year the mean cost μμ for a one-bedroom rental in a certain city was $1,200 per month. Eli is looking for a one-bedroom apartment and is investigating whether the mean cost is less now than what it was last year. A random sample of apartments had a sample mean x−x− of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation. Which of the following is the correct set of hypotheses?
NOT Ho:μ=1,200Ho:μ=1,200 Ha:μ>1,200Ha:μ>1,200
A chi-square goodness-of-fit test where all assumptions were met yielded the test statistic χ2=12.4χ2=12.4. Henry claims the corresponding p-value of 0.03 means that the probability of observing a test statistic of χ2=12.4χ2=12.4 is 0.03, assuming the null hypothesis is true. Which of the following is a valid criticism of this interpretation of the p-value?
NOT The significance level is not stated.
polling randomly selected responding stuff
NOT two fractions, bottom of each is a square.
A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was χ2=8.2χ2=8.2. Which of the following represents the p-value for the test?
P(χ2≥8.2)=0.04
An administrator at a local high school wanted to investigate whether there is an association between the amount of time a student studies for a test and the type of extracurricular activity the student is involved in. Three hundred students selected at random were asked how long they had studied for the last math test and how many extracurricular activities they are involved in. The times they had studied were recorded as either not at all, less than 30 minutes, or more than 30 minutes. Each student also identified which extracurricular activity (out of a total of 5 extra curricular activities) they were involved in. The calculated chi-square test statistic was 7.53 with a corresponding p-value of 0.4807. Based on this p-value, which of the following is the correct decision for the appropriate hypothesis test at the α=0.05α=0.05 significance level?
Fail to reject the null hypothesis. The test is not statistically significant because a p-value of 0.4807 is greater than a significance level of 0.05.
maria railroad crossing routes trains
NOT The p-value is greater than a, and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes.
A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?
Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
Type of Grass SeedPercentFescue (F)55%Buffalo grass (B)22%Blue grama (BG)10%Indian grass (I)7%Green needlegrass (NG)6% A quality control specialist tests samples of the seed being packaged and uses a chi-square goodness-of-fit test to see whether the proportions in the samples match what is claimed by the company. Which of the following best describes the null hypothesis and the alternative hypothesis for the test?
Ho:pF=0.55,pB=0.22,pBG=0.10,pI=0.07,pPNG=0.06Ho:pF=0.55,pB=0.22,pBG=0.10,pI=0.07,pPNG=0.06 Ha:Ha:At least one of the proportions is different
Which of the following is an appropriate description of the chi-square distribution?
NOT A chi-square distribution will only contain positive values and will be skewed right, with the skew becoming more pronounced with increasing degrees of freedom. NOT A chi-square distribution will contain positive and negative values, and will be skewed right, with the skew becoming less pronounced with increasing degrees of freedom.
Random samples of players for two types of video games were selected, and the mean number of hours per week spent playing the games was calculated for each group. The sample means were used to construct the 90 percent confidence interval ( 1.5, 3.8 ) for the difference in the mean number of hours per week spent playing the games. The maker of one of the video games claims that there is a difference in the population mean number of hours per week spent playing the two games. Is the claim supported by the interval?
NOT Yes, because the midpoint of the interval is greater than 1.
A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?
0.29,1000(0.29)(0.71) the one where it's divided by 1000
A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
$432.00
Each of 133 children in a sample was asked to choose a pencil. Three different colors were available: yellow, red, and blue. The number of 2-year olds and 3-year olds who selected each color is shown in the table above. In a test of independence of age and color, which of the following is used as the expected cell count for 2-year olds who select a yellow pencil?
133(14+28)(14+32+19)
A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim?
3
To determine whether employees at Site X have higher salaries, on average, than employees at Site Y of the same company do, independent random samples of salaries were obtained for the two groups. The data are summarized below. Based on the data, which of the following statements is true?
NOT At the 10% significance level, there is no significant difference in salaries between the employees at the two sites.
A 99 percent confidence interval for a difference in means was given as 25.1±4.3.25.1±4.3. Assuming all conditions for inference were met, which of the following is a correct interpretation of the 99 percent confidence level?
NOT In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will capture the difference in sample means.
A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true?
NOT Neither the probability of a Type II error nor the power of the test would change.
coins question. probability and normalcy
No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough.
A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20 percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Assuming the conditions for inference are met, what is the test statistic for a chi-square goodness-of-fit test to investigate whether the distribution of the sample is consistent with the company's claim?
χ2=10(6−10)2+30(32−30)2+10(12−10)2
A spinner made for a game of chance has 8 equally likely spaces. Alfonso records the result of a sample of 400 spins. Alfonso decides to calculate a chi-square test statistic for a goodness-of-fit test to see whether the spinner is fair. Which of the following is the appropriate null hypothesis?
Ho:p1=0.125,p2=0.125,p3=0.125,p4=0.125,p5=0.125,p6=0.125,p7=0.125,p8=0.125 regular equal sign
Researchers investigated whether there is a difference between two headache medications, R and S. Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication. Have the conditions been met for inference with a confidence interval for the difference in population means?
Yes, all conditions have been met.
How are the expected counts calculated when a chi-square goodness-of-fit test is conducted?
NOT The expected counts are calculated by multiplying each proportion in the alternative hypothesis by 100. NOT The values observed from the sample are the expected counts.
In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses. YesNoTotalAcupuncture41 (37.2)37 (40.8)78Placebo treatment32 (35.8)43 (39.2)75Total7380153 Which of the following is true about the chi-square test for homogeneity?
Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
The Attila Barbell Company makes bars for weight lifting. The weights of the bars are independent and are normally distributed with a mean of 720 ounces (45 pounds) and a standard deviation of 4 ounces. The bars are shipped 10 in a box to the retailers.The weights of the empty boxes are normally distributed with a mean of 320 ounces and a standard deviation of 8 ounces. The weights of the boxes filled with 10 bars are expected to be normally distributed with a mean of 7,520 ounces and a standard deviation of
NOT 8080 ounces
Which of the following is the best interpretation of the power of a significance test?
NOT Power is the probability of not detecting an effect if no effect exists.
A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?
NOT Uniform OR Bimodal
A town manager is interested in comparing requests for various town-provided services (such as street maintenance and garbage pickup) with nationally published proportions of requests for the same services. Each request in a random sample of 500 service requests from the town was classified into one of 10 different categories. Which of the following tests could be used to determine whether the proportions of service requests classified into the 10 service categories for the town differ from national proportions?
A chi-square goodness-of-fit test
A manufacturer claims its Brand A battery lasts longer than its competitor's Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table below. Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand A batteries do, in fact, last longer than Brand B batteries?
NOT A one-sided, two-sample z-test
The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ( $1,288, $2,586 ) With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval?
NOT A sample mean greater than $1,937
Educators are testing a new program designed to help children improve their reading skills. The null hypothesis of the test is that the program does not help children improve their reading skills. For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help. Which of the following should the researchers do to avoid the more consequential error?
NOT Decrease the significance level to decrease the standard error.
Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type I error that could result from the test?
NOT The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is 11 ounces.extra
At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?
Sampling without replacement will result in a standard deviation less than but close to 0.4(0.6)500.5000.4(0.6).
A reporter intends to survey residents of a city to investigate whether there are differences in use of grocery delivery services by region of the city where the residents live (north, south, west, and east). City residents will be asked to respond yes or no to the question "Do you regularly use a grocery delivery service to purchase groceries?" Results will be collected in a 4-by-2 table of counts organized by region and response to the question. For a chi-square test for homogeneity, which of the conditions listed below is not necessary to investigate whether there are differences between use of grocery delivery service by region?
The number of residents sampled from each region should be greater than 30.
A χ2χ2 goodness-of-fit test was used to test the hypothesis that students at a local university select majors in the same proportions as other universities in the state. A chi-square test statistic of χ2=45.6χ2=45.6 was calculated with a corresponding p-value of 0.005. Which of the following is correct?
There is sufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
To investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. The residents were asked which candidate they preferred, and each resident was classified into one of three age-groups. The test statistic for the appropriate hypothesis test was 3.7408. Approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference?
NOT 0.5873 NOT 0.2908 NOT 0.7117
A group of men and women were surveyed to investigate the association between gender and the number of friends the person has on a social media Web site. Results are shown in the table below. Which of the following procedures is the most appropriate for investigating whether an association exists between gender and the number of friends a person has on a social media Web site?
NOT A t-test for the slope of the regression line OR A matched-pairs t-test for a mean difference NOT A two-sample t-test for the difference between means
Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table. Observed Number of Nests per Birdhouse by Location 0 nests1 nest2 or 3 nestsTotalGolf3042880Nongolf405822120Total7010030200 If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouses with 1 nest in nongolf locations?
60
Jimmy likes to listen to a variety of music. His library has the following distribution of music genres. Music TypeCountryR&BPopRetroRockPercent22%10%12%20%36% Jimmy believes that the shuffle feature on his music player is malfunctioning by not playing songs that meet this distribution of music types. To test this, he listens to 100 songs randomly chosen when his player is in shuffle mode and records the number of songs in each category. Which inference procedure should he use to test whether or not the shuffle feature is working correctly?
A chi-square goodness-of-fit test
A polling organization uses random digit dialing of registered voters in a county to gauge the voters' opinions about a ballot initiative to increase taxes that would pay for a new county park. The polling organization will investigate whether there are differences in how voters respond based on the highest level of education completed. The phone survey asked the voters contacted whether they approve or disapprove of the tax increase. The voters were also asked to indicate their highest level of education completed: high school, bachelor's degree, or master's degree. Which of the following is the appropriate test to investigate whether there is an association between opinion about the ballot initiative and highest level of education completed?
A chi-square test of independence
A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered. Animal typeDogsCatsLivestockBirdsOtherPercent61%22%8%6%3% If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?
Animal TypeDogsCatsLivestockBirdsOtherExpected140.350.618.413.86.9
At a large regional collegiate women's swim meet, an official records the time it takes each swimmer to swim 100 meters for all swimmers who compete in only one stroke category. The following table shows the mean times and corresponding standard deviations for the collegiate women at the swim meet for each of the four stroke categories. Stroke CategoryMean 100 meter TimeStandard DeviationBackstroke55.6 seconds0.70 secondsBreaststroke63.3 seconds0.92 secondsButterfly54.4 seconds0.94 secondsFreestyle50.2 seconds0.76 seconds For each of the 4 stroke categories, consider a random variable representing the time of a randomly selected swimmer in that category. What is the standard deviation of the sum of the 4 random variables?
3.32 seconds
A large factory that builds machines has three shifts, one that starts at 4:00 A.M., one that starts at noon, and one that starts at 8:00 P.M. The manager of the factory wanted to know whether there is an association between an employee's work experience (less than five years with the company, between five and twenty years with the company, over twenty years with the company) and the time of the employee's shift. The manager selected a random sample of 125 employees and classified employees by their shift time and work experience. Which of the following is an appropriate pair of hypotheses for the manager to use?
Ho:Work experience is independent of the time of an employee's shift. Ha:Ha:Work experience is dependent on the time of an employee's shift.
A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim. Ho:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11Ho:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11 In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples?
NOT n≥30 NOT n≥46 NOT 30≤n≤5030≤n≤50
A business analyst is investigating whether the mean amount of purchases made by customers at an online department store is greater than $100. The analyst obtained a random sample of 56 orders and calculated a sample mean of $102.30 and a sample standard deviation of $5.30. Which of the following is an appropriate test for the investigation?
NOT A matched-pairs t-test for a mean difference
The mayor of a large city will run for governor if he believes that more than 30 percent of the voters in the state already support him. He will have a survey firm ask a random sample of n voters whether or not they support him. He will use a large sample test for proportions to test the null hypothesis that the proportion of all voters who support him is 30 percent or less against the alternative that the percentage is higher than 30 percent. Suppose that 35 percent of all voters in the state actually support him. In which of the following situations would the power for this test be highest?
NOT The mayor uses a significance level of 0.01 and n = 250 voters.
Which of the following is not a condition for a chi-square goodness-of-fit test?
The distribution of the sample should be approximately normal.
A polling agency conducted a survey about social media in which each person in random samples of 1,000 men and 1,000 women was asked what factor he or she considers to be the most important when deciding whether to connect on social media with another person. The responses are shown in the table. Factor Personal FriendStay in TouchMutual FriendsBusiness NetworkingOtherMen6002101054540Women650224651546 What is the contribution to the chi-square test statistic for men who selected business networking as the most important factor
7.5
Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample. Which of the following is an appropriate test for the researchers' hypothesis?
A one-sample t-test for a population mean
Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1? The mean The median The standard deviation
NOT I and II only OR I only
A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows pictures of rooms decorated with three different color scheme to each person in a random sample of 110 men and to each person in a random sample of 90 women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test for homogeneity of proportions will be used to test the consultant's hypothesis. Assuming that the conditions for inference are met, which of the following statements is true for the test?
The more that men and women differ in their color preferences, the larger the chi-square statistic will be.
Nonnative speakers of English often have characteristics in their handwriting that differ depending on the speaker's first language. Handwriting samples from a random sample of Chinese, Malay, and Indian children in a school in Singapore were taken to investigate these differences. One characteristic of interest was a rounding at the top of the capital letter A. Data for the top-rounding characteristic for a sample of 153 children are shown in the table. Observed Top Rounding on the Capital Letter A MalayIndianChineseTotalYes 921 8 38No423142115Total515250153 If children from these countries exhibit top rounding in the same proportions, what is the expected count for Malay children who show top rounding?
(153(38)(51))
A company ships gift baskets that contain apples and pears. The distributions of weight for the apples, the pears, and the baskets are each approximately normal. The mean and standard deviation for each distribution is shown in the table below. The weights of the items are assumed to be independent. Let the random variable W represent the total weight of 4 apples, 6 pears, and 1 basket. Which of the following is closest to the standard deviation of W ?
1.97 ounces
Let X be a random variable whose values are the number of dots that appear on the uppermost face when a fair die is rolled. The possible values of X are 1, 2, 3, 4, 5, and 6. The mean of X is 7/2 and the variance of X is 35/12. Let Y be the random variable whose value is the difference (first minus second) between the number of dots that appear on the uppermost face for the first and second rolls of a fair die that is rolled twice. What is the standard deviation of Y ?
3512+35121235+1235 not just the adding one
A factory produces bags of rubber bands. A bag of rubber bands has five different sizes: extra large (XL), large (L), medium (M), small (S), and extra small (XS). A quality control specialist collects a random sample of 450 rubber bands from the bagging machine and calculates a chi-square goodness-of-fit test to see if the frequencies for each size in the sample match the hypothesized distribution. The quality control specialist will test his sample against the following null hypothesis Ho:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10Ho:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10 How many medium rubber bands are expected in the random sample of 450 rubber bands?
180
Each person in a random sample of adults indicated his or her favorite color. The results, shown in the table below, are reported by age group of the respondents. If choice of color is independent of age group, which of the following expressions is equal to the expected number of respondents who are aged 30 to 50, inclusive, and prefer green?
314(99)(108)
Students in a high school statistics class wanted to see if the distribution of the colors of a popular candy was different in the bags for different types of candies the company manufactures. The students purchased several large bags of regular candies, tropical-flavored candies, and sour-flavored candies. For each type of candy, the students took a random sample of 100 candies and recorded how many of each color (red, green, yellow, or blue) were in the sample. The students verified the conditions for inference and calculated a chi-square test statistic of 12.59 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value in the context of the test?
Assuming that the distribution of colors for the different types of candies is the same, there is a 5 percent chance of finding a test statistic of 12.59 or larger.
A fisheries biologist collected a random sample of fish from a lake and conducted a chi-square goodness-of-fit test to see if the distribution of fish changed over time. The table below shows the distribution of fish that were put into the lake when it was originally stocked. Fish TypeTroutBassPerchSunfishCatfishPercent25%25%20%15%15% The biologist found evidence to reject the null hypothesis in favor of the alternative hypothesis. Which of the following represents the alternative hypothesis of the test?
At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked.
A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?
Both np and n(1 - p) are at least 10
A candy company claims that 10 percent of its candies are blue. A random sample of 200 of these candies is taken, and 16 are found to be blue. Which of the following tests would be most appropriate for establishing whether the candy company needs to change its claim?
One-sample proportion z-test
Which of the following is a reason not to use a chi-square test of homogeneity to analyze a set of data?
The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.
A human resources manager selected a random sample of 200 workers who donate to charity. The following table shows the distribution of the 200 workers. Type of workerCountManagement96Other white collar50Blue collar54 The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample?
The expected number of management workers donating to charity is 100.
To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)?
0.7−0.6(0.65)(0.35)(150+160)(0.65)(0.35)(501+601)0.7−0.6 the 7 and six on top of the square of the decimals multiplied by each other, times the two fractions added together
A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by-4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age-group. Which of the following is the appropriate test for the investigation?
A chi-square test of independence
To investigate whether there is a significant difference between two regions of a state in the percent of voters who intend to vote for the incumbent governor in the next election, a polling agency interviewed 300 randomly selected voters from the north of the state and 400 randomly selected voters from the south of the state. Of those interviewed, 200 from the north and 325 from the south indicated they intended to vote for the incumbent governor in the next election. Which of the following is the most appropriate method for analyzing the results?
NOT A one-sample z-test for a population proportion NOT A one-sample z-test for a sample proportion
The manager of a restaurant tracks the types of dinners that customers order from the menu to ensure that the correct amount of food is ordered from the supplier each week. Data from customer orders last year suggest the following weekly distribution. The manager believes that there might be a change in the distribution from last year to this year. A random sample of 200 orders was taken from all customer orders placed last week. The following table shows the results of the sample. Assume each order is independent. For which type of dinner is the value of its contribution to the appropriate test statistic the greatest?
NOT Chicken
A car company claims that its new car, the GoFast2000, has a gas mileage of 35 miles per gallon (mpg). A consumer group suspects that the true mean gas mileage of the new cars is less than 35 mpg. The group tests 50 randomly selected GoFast2000 cars and finds a sample mean of 34.8 mpg. With all assumptions for inference met, a hypothesis test resulted in a p-value of 0.324. For a significance level of α=0.05,α=0.05, which of the following is a correct conclusion?
NOT The p-value is greater than 0.05, and the null hypothesis is rejected. There is not convincing statistical evidence that the mean is less than 35 mpg.
n investigator was studying a territorial species of Central American termites, Nasutitermes corniger. Forty-nine termite pairs were randomly selected; both members of each of these pairs were from the same colony. Fifty-five additional termite pairs were randomly selected; the two members in each of these pairs were from different colonies. The pairs were placed in petri dishes and observed to see whether they exhibited aggressive behavior. The results are shown in the table below. A Chi-square test for homogeneity was conducted, resulting in x2 = 7.638. The expected counts are shown in parentheses in the table. Which of the following sets of statements follows from these results?
x2 is significant, p < 0.01; the counts in the table suggest that termite pairs from different colonies are less likely to be aggressive than termite pairs from the same colony.
A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : µ = 12 versus Ha : µ < 12 was conducted, where µ represents the population mean number of ounces of the beverage dispensed per bottle by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05?
NOT Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
The manager of the cafeteria at a local high school wanted to see if there was an association between a student's grade level and whether the student approves of the food choices in the cafeteria. The manager selected a random sample of students and asked if they approved of the food choices and also recorded the grade levels of the students. If a student was in ninth or tenth grade, he or she was labeled as an underclassman, and if the student was in eleventh or twelfth grade, he or she was labeled as an upperclassman. The table shows the results of the survey. UnderclassmanUpperclassmanTotalApproves of the Cafeteria Food502070Does Not Approve of the Cafeteria Food306090Total8080160 Assuming that all conditions for inference have been met, which of the following equations gives the appropriate chi-square test statistic and the correct number of degrees of freedom to determine if there is an association between grade level and whether a student approves of the food choices in the cafeteria?
χ2=35(50−35)2+45(20−35)2+45(30−45)2+45(60−45)2 with 1 degrees of freedom
A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has mean 14.1 pounds and standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has mean 6.7 pounds and standard deviation 0.5 pound. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W ?
10(1.3)2+15(0.5)2
The following question(s) refer to the following information.Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?
$9.40
Data were collected on the ages, in years, of the men and women enrolled in a large sociology course. Let the random variables M and W represent the ages of the men and women, respectively. The distribution of M has mean 20.7 years and standard deviation 1.73 years. The distribution of W has mean 20.2 years and standard deviation 1.60 years. Of all of those enrolled in the course, 54 percent are men and 46 percent are women. What is the mean age of the combined distribution of both men and women in the course?
NOT 20.47 years NOT 40.9
A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to the banning of trans fats. Is there convincing statistical evidence of a difference between the two population proportions at the significance level of 0.05 ?
NOT Yes, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is less than 0.05.
Hannah wanted to investigate whether there was a difference in the time spent in the checkout line between two grocery stores in a large city. She went to Grocery Store J on a Monday morning and recorded the time, in minutes, it took 30 customers to go through a checkout line. Then she went to Grocery Store K on Monday afternoon and recorded the time it took 30 customers to go through a checkout line. Hannah calculated the mean number of minutes for the customers in each line. She intends to conduct a two-sample t-test for a difference in means between the two stores. Have all conditions for inference been met?
NOT No, the sample sizes are not large enough to assume normality of the sampling distribution.
The National Park Service writes materials for students to use while in the parks. In a study of the effectiveness of some of these materials, a random sample of students was selected to take a short quiz about oak trees after using these materials. A random sample of park professionals also took the quiz. Investigators compared classifications (low, medium, and high) of the crown shapes—the general shapes of the leafy parts of the trees—made by students in s 6 through 12 with classifications made by professionals. Data from the study are shown in the table. ProfessionalsStudentsTotalLow544397Medium483987High7916Total10991200 If the professionals and the students do not differ in the distributions of their responses, which of the following is equal to the expected number of students who classify the crown shapes as medium?
(200(87)(91))
Sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question - agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have?
4
A simple random sample of 1,000 United States adults was collected to investigate whether gender and being a coffee drinker are independent. The results are summarized in the table with the expected counts shown in parentheses. Coffee Drinker? YesNoTotalGenderMale191 (148.5)299 (341.5)490Female112 (154.5)398 (355.5)510Total3036971,000 Which statement is true about whether the conditions for the chi-square test for independence have been met?
All necessary conditions are satisfied to apply a chi-square test for independence between gender and being a coffee drinker.
A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?
NOT 14.5 OR 15.0
A study will be conducted to investigate whether there is a difference in pain relief for two brands of headache pills, N and P. Participants will be randomly assigned to one of two groups. One group will take pill N when they experience a headache, and the other group will take pill P when they experience a headache. Each participant will record the number of minutes it takes until relief from the headache is felt. The mean number of minutes will be calculated for each group. Which of the following is the appropriate test for the study?
NOT A matched-pairs t-test for a mean difference
A physician believes that the exercise habits of East Coast adults are different from the exercise habits of West Coast adults. To study this, she gathers information on the number of hours of exercise per week from a random sample of East Coast adults and a random sample of West Coast adults. Which of the following might be an appropriate null hypothesis for this study?
NOT The average number of hours of exercise per week for East Coast adults is greater than the average number of hours of exercise per week for West Coast adults. NOT The probability is 0.5 that an East Coast adult and a West Coast adult exercise an equal number of hours per week.
A controversial issue in the sport of professional soccer is the use of instant replay for making difficult goal line decisions. Each person in a representative sample of 102 players, fans, coaches, and officials was asked his or her opinion about the use of instant replay for goal-line decisions. The data are summarized in the two-way frequency table below. In testing to see whether opinion with respect to the use of instant replay is independent of the category of the person interviewed, a chi-square test statistic of 27.99 and a p-value less than 0.001 were calculated. Which of the following statements is correct?
NOT The null hypothesis states that there is an association between category and opinion about the use of instant replay, and the small p-value suggests that the null hypothesis should be rejected. NOT The chi-square test shows that fans favor the use of instant replay.
Consider a situation in which sampling without replacement is used to generate a random sample from each of two separate populations. To calculate a confidence interval to estimate the difference between population proportions, which of the following checks must be made?
NOT Each sample proportion value must be less than or equal to 0.5.
A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?
135 males and 147 females
A survey was conducted in which both men and women were asked a question about a current issue. Possible responses to this question were "in favor of," "not in favor of," or "no opinion." A chi-square test is to be used to determine whether the response to this question is independent of gender. The number of degrees of freedom for the chi-square test in this situation is
2
Two college roommates have each committed to donating to charity each week for the next year. The roommates' weekly incomes are independent of each other. Suppose the amount donated in a week by one roommate is approximately normal with mean $30 and standard deviation $10, and the amount donated in a week by the other roommate is approximately normal with mean $60 and standard deviation $20. Which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $120 ?
5 weeks
Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?
2.415
In order to plan its next advertising campaign, the Trendy Motor Vehicle Company is investigating whether the type of vehicle and the color of vehicle are related. Each person in a random sample of size 275 selected from the company's mailing list was classified according to the type (car or truck) and the color of vehicle he or she drove. The data are shown in the table below. Which of the following procedures would be most appropriate to use for investigating whether there is a relationship between vehicle type and color?
A two-sample t-test
Most dermatologists recommend that the ideal shower lasts approximately 10 minutes. A researcher suspects that the average shower length of high school students is greater than 10 minutes. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 minutes. With all conditions for inference met, a hypothesis test was conducted at the significance level of α=0.05,α=0.05, and the test produced a p-value of 0.0000. Which of the following is an appropriate conclusion?
NOT The researcher has statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.
Ms. Harper knows that her students in a computing course can choose from one of three operating systems for the semester: Doors, Banana, or Duix. Ms. Harper wants to test the hypothesis that her students will select the operating systems in the same proportion as students in other computing courses at the university. She conducts a χ2χ2 goodness-of-fit test and calculates χ2=3.79χ2=3.79with a corresponding p-value of 0.15. Which of the following is correct at a 5-percent level of significance?
Fail to reject the null hypothesis, since 0.15 > 0.05.
Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded. Are the sample sizes large enough to assume that the sampling distribution of the difference in sample proportions is approximately normal?
NOT No. The sample size for drug X is large enough, but the sample size for drug Y is not. NOT There is not enough information provided to determine whether the sampling distribution is approximately normal.
A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?
NOT t=28+324,0002+3,5002(58,000−55,000)
Which of the following chi-square distributions has the smallest number of degrees of freedom?
hump all the way to the left
A national health study reported that the proportion of students with elevated blood pressure is 0.15. The principal of a local high school believes that the proportion of students in the school with elevated blood pressure is greater than 0.15. If a large random sample is used, which of the following is the most appropriate test to investigate the principal's belief?
A z-test for a proportion
For which of the following is a chi-square goodness-of-fit test most appropriate?
Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution
A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W represent the total amount won, where W = X - 15. What is the mean of W?
NOT -$10.50
A company claims it audits its employees' transactions based on their job level. For entry-level positions, the company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds χ2=0.771χ2=0.771 with a corresponding p-value of 0.68. Assuming conditions for inference were met, which of the following is the correct interpretation of the p-value?
NOT There is a 68 percent chance that the company's claim is correct. OR If the null hypothesis were true, there would be a 68 percent chance that the company's claim is correct. OR There is a 68 percent chance of obtaining a chi-square value of at least 0.771. OR If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of 0.771.
A state highway commission is considering removing the lane that allows people to pay cash for a toll on a toll road and requiring all people who use the toll road to pay with an electronic transponder that is connected to their car. The commission wants to know whether the proportion of people who live in the northern part of the state and are in favor of removing the cash lane is different from the proportion of people who live in the southern part of the state and are in favor of removing the cash lane. Independent random samples are selected from the northern and southern parts of the state. The table summarizes the responses of those surveyed. NorthernSouthernTotalRemove Cash Lanes11298210Keep Cash Lanes89105194Total201203404 Which of the following is closest to the p-value of the appropriate test to investigate whether the proportion of people living in the northern part of the state who are in favor of removing the cash lane is different from the proportion of people living in the southern part of the state who are in favor of removing the cash lane?
0.1342
A two-sample t-test for a difference in means will be conducted to investigate whether the average length of a cell phone call is shorter this year compared with 5 years ago. From a random sample of 35 phone call records this year, the average length was 25 minutes with a standard deviation of 4 minutes. From a random sample of 32 phone call records from 5 years ago, the average length was 27 minutes with a standard deviation of 5 minutes. The difference (this year minus five years ago) in means will be calculated. With a null hypothesis of no difference in length, which of the following is a correct test statistic for the test?
NOT t=354+32527−25
A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?
17.5
Consider the results of a hypothesis test, which indicate there is not enough evidence to reject the null hypothesis. Which of the following statements about error is correct?
NOT Both types of error could have been made, but the probability of a Type I error is less than the probability of a Type II error. NOT Both types of error could have been made, but the probability of a Type I error is greater than the probability of a Type II error.
A forester reported the following distribution of tree types to a local logging company. Tree TypeSprucePineFirDeciduousOtherPercent52%22%8%10%8% The logging company generated a random sample of 100 trees and observed the following distribution of trees in each of the categories. Tree TypeSprucePineFirDeciduousOtherObserved Count51211099 The logging company would like to use its sample to provide convincing statistical evidence that over 50 percent of the trees in the forest are spruce trees. The logging company has decided to use a chi-square goodness-of-fit test to justify its claim. Why is the chi-square goodness-of-fit test not an appropriate procedure for the logging company to use?
A chi-square goodness-of-fit test would be used to show that the entire distribution of trees in the forest is different than what the forester reported, not necessarily the individual proportion representing the spruce trees.
According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)
NOT P(z>(0.27)(0.73)0.22−0.27) OR P(z>(0.27)(0.73)0.22−0.27)
At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a randomly selected loan agent closes on a randomly selected day has the probability distribution below. x1234567P(x)0.050.100.220.300.180.120.03 At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true?
The mean daily salary is greater than $350 per day.
Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends' scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in a single game?
NOT 0.28
To test the durability of cell phone screens, phones are dropped from a height of 1 meter until they break. A random sample of 40 phones was selected from each of two manufacturers. The phones in the samples were dropped until the screens broke. The difference in the mean number of drops was recorded and used to construct the 90 percent confidence interval ( 0.46, 1.82 ) to estimate the population difference in means. Consider the sampling procedure taking place repeatedly. Each time samples are selected, the phones are dropped and the statistics are used to construct a 90 percent confidence interval for the difference in means. Which of the following statements is a correct interpretation of the intervals?
NOT Approximately 90 percent of the intervals constructed will capture the difference in sample means.
An airline claims that the mean flight time between City X and City Y is 38 minutes. After taking many flights, a local business group believes that the claim is unrealistic and that the actual mean flight time is greater than 38 minutes. If the group conducts a study to investigate its belief, which of the following hypotheses should be tested?
NOT H0: x̅ = 38, versus Ha : x̅ > 38 NOT H0: x̅ = 38, versus Ha : x̅ < 38
Polling organizations regularly collect data on the public's opinions and habits. A question on a recent survey asked, "How often do you purchase coffee from a coffeehouse?" There may be differences in how people respond to this question based on whether the person is a full-time student. Suppose a polling organization uses random digit dialing of local phone numbers to take a poll and asks respondents whether they are full-time students. In addition, they ask respondents to identify how often they purchase coffee from a coffeehouse (never, once a week, two to three times a week, daily, more than once a day). The data are collected in a 5-by-2 table of counts. Which of the following is the appropriate null hypothesis when conducting a chi-square test for the data?
NOT Ho: The proportion of people for each category in the 5-by-2 table will be 10 percent. NOT Ho:Ho: For each purchasing frequency, the proportion of full-time students is different. NOT Ho: How often a person purchases coffee from a coffeehouse is dependent on whether a person is a full-time student.
A chi-square test was conducted to investigate whether there is an association between a person's favorite flavor of ice cream and their favorite toppings. Each of 200 randomly selected customers at an ice cream parlor was asked to pick their favorite flavor from vanilla, chocolate, chocolate chip, or none of these. They were also asked to pick their favorite topping from chocolate sauce, peanuts, crumbled cookies, crushed candies, or none of these. The hypothesis test had a test statistic of 24.97 with an associated p-value of 0.015. If the significance level of the test was α=0.05α=0.05, which of the following is the correct decision for this hypothesis test?
There is convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
The district manager of four different restaurants wanted to investigate whether the four restaurants differed with respect to customers ordering dessert or not based on family classification (with children or without children). Independent random samples of 100 customers who ordered dessert were selected from each restaurant, and the customers were identified as either being with children or without children. After verifying the conditions for the appropriate hypothesis test, the manager calculated a chi-square test statistic of 6.45 with an associated p-value of 0.092. Based on the p-value and α=0.05.α=0.05. what conclusion should the manager make regarding the proportion of customers who order dessert at each restaurant and the customers' family classification?
There is not convincing statistical evidence to suggest that the proportion of customers who order dessert at each restaurant is not the same based on family classification.
A statistician is conducting a chi-square goodness-of-fit test and is limited by the cost, per individual, to conduct the study. The statistician selects a sample of size 39, which is the smallest sample possible that will meet the condition for large expected counts. Which of the following could not be the null hypothesis for the study?
NOT Ho:p1=0.15,p2=0.35,p3=0.22,p4=0.15,p5=0.13Ho:p1=0.15,p2=0.35,p3=0.22,p4=0.15,p5=0.13 NOT Ho:p1=0.24,p2=0.23,p3=0.21,p4=0.18,p5=0.14 OR Ho:p1=0.34,p2=0.21,p3=0.14,p4=0.15,p5=0.16
An administrator at a local high school wants to investigate whether there is an association between the grade level of a student (either ninth, tenth, eleventh, or twelfth) and how the student commutes to school (either walks, bikes, takes the bus, receives a ride, or drives). After a chi-square test for association was conducted, the results indicated that the chi-square test statistic was 14.63 with a p-value of 0.2623. Which of the following is the correct interpretation of the p-value in the context of the test?
NOT Assuming that a student's grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger. NOT There is a 26.23 percent chance that there is no association between grade level and how a student commutes to school. NOT Assuming that a student's grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or smaller.
The table below shows historical data for the distribution of the number of customers, in half-hour time periods, who visit the electronics department of a retail store. For example, in 25 percent of the time periods for which data were collected, no customers were observed in the electronics department of the store. To investigate if the distribution has changed, the number of customers who visited the electronics department of the store was recorded for each of 50 randomly selected time periods. The results are shown in the table below. A chi-square goodness-of-fit test was conducted to determine whether the data provide convincing evidence that the distribution has changed. The test statistic was 10.13 with a p-value of 0.0175. Which of the following statements is true?
NOT At the significance level α = 0.10, the data do not provide convincing evidence that the current distribution is different from the historical distribution. OR No valid conclusion can be made because the observed frequency for one cell is less than 5. OR The mean number of customers in a randomly selected time period is 12.5. OR The chi-square statistic has 50 - 1 = 49 degrees of freedom.
Two siblings, Alice and Sean, are both convinced that they are faster than the other at solving a puzzle cube. They recorded the length of time it took them to solve the cube 18 times each during a one-month period. Then each calculated the mean amount of time and standard deviation, in minutes, for their times. Let μAμA equal the mean time it took Alice to solve the puzzle cube and μSμSequal the mean time it took Sean. Which of the following are the appropriate null and alternative hypotheses to test for a difference in time for the siblings to solve the cube?
NOT Ho:x‾A−x‾S=0Ho:xA−xS=0 Ha:x‾A−x‾S>0Ha:xA−xS>0
An experiment was conducted to determine whether the price of a golf club affected the distance a golfer could hit a golf ball. A sample of 60 golfers were randomly assigned to one of two groups, C or E. The 30 golfers in group C were given a club and told the price of the club was cheap; the 30 golfers in group E were given the same club and told the price of the club was expensive. In reality, there was no difference in price. The golfers used their assigned clubs to hit a golf ball as far as they could. The distance, in yards, that each golfer hit the golf ball was recorded, and the mean distance calculated for each group. A two-sample t-test for a difference in means will be conducted. Which of the following statements are true? The data were collected using random assignment. The data were collected using random selection. The distribution of the difference in sample means will be approximately normal.
NOT I only
A political scientist claims that negative advertising on television affects younger voters more than it affects older voters. To test this claim, the scientist obtained data from two random samples of voters categorized into two age-groups, older and younger. The null hypothesis was that there was no difference in the proportions of voters in the two age-groups who would be affected by negative ads. The alternative hypothesis was that the proportion of younger voters affected would be greater than the proportion of older voters affected. Assuming all conditions for inference were met, the scientist conducted the test at a significance level of α=0.05α=0.05. The resulting p-value was 0.206. Which of the following is the correct decision for the test?
NOT The p-value is less than αα, and the null hypothesis is rejected. There is convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. NOT The p-value is greater than \(\alpha)\, and the null hypothesis is not rejected. There is convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters.