AP Stats Final
A significance test was performed to test H0: μ=2H0: μ=2 versus the alternative Ha: μ≠2Ha: μ≠2. A sample of size 28 produced a standardized test statistic of t=2.051t=2.051. Assuming all conditions for inference were met, which of the following intervals contains the P-value for this test?
0.05<P<0.10
In a test of H0:p=0.4H0:p=0.4 against Ha:p≠0.4Ha:p≠0.4, a random sample of size 100 yields a standardized test statistic of z=1.28z=1.28. Which of the following is closest to the P-value for this test?
0.20
What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?
0.4
A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4 shapes incorrectly but gets the fifth one correct?
(4/5)^4 x (1/5)
A confidence interval for a difference in proportions is −0.077 to 0.013. What are the point estimate and the margin of error for this interval?
-0.032, 0.045
Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital's capacity will be exceeded?
0.035
Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren't really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren't ill. Which of the following is a 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren't ill?
0.03±1.96
We compute the value of the χ2χ2 test statistic to be 6.57. Assuming that the conditions for inference are met, which of the following is correct?
0.05 < P-value < 0.10
Suppose we select an SRS of size n=100n=100 from a large population having proportion p of successes. Let ˆpp^ be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of ˆpp^?
0.85
Let D be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of D?
1.27
You want to compute a 90% confidence interval for the mean difference in height for mothers and their adult daughters using a random sample of 30 mothers who have an adult daughter. What critical value should you use for this interval?
1.699
Which of the following is the critical value for calculating a 94% confidence interval for a population proportion?
1.881
Assuming H0H0 is true, what is the expected number of Hispanic drivers who would receive a ticket?
11.84
To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. The results were Suspect's True StatusExaminer's DecisionInnocentGuilty"Innocent"13115"Guilty" 9125 If the hypotheses are H0H0: Suspect is innocent versus HaHa: Suspect is guilty, which of the following is the best estimate of the probability that an expert commits a Type II error?
15/140
The weights (in pounds) of three adult males are 160, 215, and 195. What is the standard error of the mean for these data?
16.07
A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean ¯xx¯. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of ¯xx¯ will be half as big as when using a sample size of 160. What sample size should the researcher use?
640
Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. Which of the following is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?
700
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true?
72% is a statistic and 56% is a parameter.
A 90% confidence interval for the mean μμ of a population is computed from a random sample and is found to be 90±3090±30. Which of the following could be the 95% confidence interval based on the same data?
90±39
The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus 3 percentage points at a 95% confidence level." You can safely conclude that
95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.
We want to construct a one-sample tt interval for a population mean using data from a population with unknown shape. In which of the following circumstances would it be inappropriate to construct the interval based on an SRS of size 14 from the population?
A boxplot shows that the values above the median are much more variable than the values below the median.
The makers of a specialty brand of bottled water claim that their "mini" bottles contain 8 ounces of water. To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle. The mean volume was 7.98 ounces and the 95% confidence interval for true mean volume is 7.93 to 8.03 ounces. Based on the sample, which of the following conclusions best addresses the makers' claim?
Because 8 is in the interval, there is not convincing evidence that their claim is incorrect.
At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference (Game - Concert) in population proportions is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher's test of the claim?
Because the interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
The figure shows the probability distribution of a discrete random variable X. Which of the following best describes this random variable?
Binomial with n=8,n=8, p=0.3
The power takeoff driveline on tractors used in agriculture can be a serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183 tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields, 15 were removed. We wish to perform a test of H0: pB = pFH0: pB = pF versus Ha: pB > pF, where pB and pFHa: pB > pF, where pB and pFare the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test?
Both populations are Normally distributed.
A 95% confidence interval for μμ based on n=15n=15 observations from a Normal population is (-0.73, 1.92).(-0.73, 1.92). If we use this confidence interval to test the hypothesis H0: μ=0H0: μ=0 against Ha: μ≠0,Ha: μ≠0, which of the following is the most appropriate conclusion?
Fail to reject H0H0 at the α=0.05 level of significance.
Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise stimulus. What are the null and alternative hypotheses for the appropriate significance test?
H0: μ=18H0: μ=18 vs. Ha: μ<18
An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are
H0:p=0.5;Ha:p>0.5
The category that contributes the largest component to the χ2χ2 test statistic is
Hispanic, with 6.16 more tickets than expected.
Which of the following statements about chi-square distributions are true? For all chi-square distributions, P(χ2≥0)=1.P(χ2≥0)=1. A chi-square distribution with fewer than 10 degrees of freedom is roughly symmetric. The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution.
I and III
A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to 18. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?" He asks listeners to go to his website and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100 people who voted, 70 answered "Yes." Which of the following conditions are violated?
I only
The conditions for carrying out the chi-square test in Exercise T12.1 are:
I, II, and III
Few people enjoy melted ice cream. Being from the sunny state of Arizona, Megan and Jenna decided to test if generic vanilla ice cream melts faster than Breyers vanilla ice cream.31 At 10 different times during the day and night, the girls put a single scoop of each type of ice cream in the same location outside and timed how long it took for each scoop to melt completely. When constructing a paired tt interval for a mean difference using these data, which of the following distributions should Megan and Jenna check for Normality? The distribution of melt time for the generic ice cream The distribution of melt time for the Breyers ice cream The distribution of difference in melt time
III only
In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion?
In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion.
A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margi
No; the margin of error only accounts for sampling variability.
The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with mean μ=10μ=10 ounces and standard deviation σ=1σ=1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is
Normal, with mean 40 ounces and standard deviation 2 ounces.
Which of the following has the smallest probability?
P(z>2)P(z>2) if z is a standard Normal random variable.
Anne claims that a store-brand fertilizer works better than homemade compost as a soil enhancement when growing tomatoes. To test her theory, she plants two tomato plants in each of five planters. One plant in each planter is grown in soil with store-brand fertilizer and the other plant is grown in soil with homemade compost, with the choice of soil determined at random. In three months, she will harvest and weigh the tomatoes from each plant. Which of the following is the correct confidence interval Anne should use to analyze these data?
Paired tt interval for μdiff
A 95% confidence interval for the proportion of viewers of a certain reality television show who are over 30 years old is (0.26, 0.35). Suppose the show's producers want to test the hypothesis H0:p=0.25H0:p=0.25 against Ha:p≠0.25Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05α=0.05 significance level?
Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25.
A Census Bureau report on the income of Americans says that, with 90% confidence, the median income of all U.S. households in a recent year was $57,005 with a margin of
The Census Bureau got the result $57,005±$742$57,005±$742 using a method that will capture the true median income 90% of the time when used repeatedly.
A significance test allows you to reject a null hypothesis H0H0 in favor of an alternative hypothesis HaHa at the 5% significance level. What can you say about significance at the 1% level?
The answer can't be determined from the information given.
Which null hypothesis would be appropriate for performing a chi-square test?
The distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at this university.
A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error?
The margin of error will be about 2 times larger.
Which of the following random variables is geometric?
The number of digits I read in a randomly selected row of the random digits table to get a 7
The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?
The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles.
Which of the following statements about the sampling distribution of the sample mean is incorrect?
The sampling distribution shows how the sample is distributed around the sample mean.
A quiz question gives random samples of n=10n=10 observations from each of two Normally distributed populations. Tom uses a table of tt distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample tt interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?
Tom's confidence interval is wider.
The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3% of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80p=0.80 at both schools. Which of the following is the best conclusion?
We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.
Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?
X=average amount of homework the student does per night;Y=student's height
Conference organizers wondered whether posting a sign that says "Please take only one cookie" would reduce the proportion of conference attendees who take multiple cookies from the snack table during a break. To find out, the organizers randomly assigned 212 attendees to take their break in a room where the snack table had the sign posted, and 189 attendees to take their break in a room where the snack table did not have a sign posted. In the room without the sign posted, 24.3% of attendees took multiple cookies. In the room with the sign posted, 17.0% of attendees took multiple cookies. Is this decrease in proportions statistically significant at the α = 0.05 level?
Yes. The P-valueP-value is 0.0340.034.
A study of road rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?
Yes; we have two independent random samples and large sample sizes.
You are thinking of conducting a one-sample t test about a population mean μμ using a 0.05 significance level. Which of the following statements is correct?
You can safely carry out the test if your sample size is at least 30.
Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50 randomly selected commercials in a given week. With the television's volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30 seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is
a paired t test for a mean difference.
The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n=250n=250 from this population, the sampling distribution of the sample proportion ˆpp^ would be
approximately Normal with mean 0.55 and standard deviation 0.03.
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0: μ=14Ha: μ<14H0: μ=14Ha: μ<14 A Type I error in this situation would mean concluding that the bags
are being underfilled when they really aren't
newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was ¯x=810x¯=810grams. This sample mean is an unbiased estimator of the mean weight μ in the population of all ELBW babies, which means that
in all possible samples of size 219 from this population, the mean of the values of ¯xx¯ will equal μ.
An SRS of size 100 is taken from Population A with proportion 0.8 of successes. An independent SRS of size 400 is taken from Population B with proportion 0.5 of successes. The sampling distribution of the difference (A−B)(A-B) in sample proportions has what mean and standard deviation?
mean=0.3; standard deviation=0.047mean=0.3; standard deviation=0.047
The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to
reduce the variability of the estimate.
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with the average time spent by students in a large city school district. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of H0: μsuburban=μcityH0: μsuburban=μcity versus a two-sided alternative.
reject H0H0 because 0.048<α=0.05.0.048<α=0.05. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the
sample size is sufficiently large (for any population).
Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is $80. If it comes up tails, your pay for the week is $40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings ¯xx¯. The shape of the sampling distribution of ¯xx¯ will be
symmetric but not Normal.
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with the average time spent by students in a large city school district. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of H0: μsuburban=μcityH0: μsuburban=μcity versus a two-sided alternative.
t=(6−5)−0√3260+2240t=(6−5)−03260+2240
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
using α=0.05 instead of α=0.01
Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of H0: μT−μP=0H0: μT−μP=0 versus Ha: μT−μP>0,Ha: μT−μP>0, where μT=μT= the true mean reduction in blood pressure when taking the natural product and μP=μP= the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least 7 points more, on average, than the placebo. If groups of size 50 are used in the experiment, a two-sample t test using α=0.01α=0.01 will have a power of 80% to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test
would be less than 80%.
A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5 versus Ha:p>0.5Ha:p>0.5 is which of the following?
z=0.59−0.5√0.5(0.5)100z=0.59−0.50.5(0.5)100
A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a randomly selected day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
μY= $75,σY= $22.50
Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct standard error for a 95% confidence interval for a difference in the population means?
√4.9245+
