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Prob and Stat Multiple Choice Final
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HHHHH
In tossing a fair coin, which of the following sequences is more likely to appear?
9
An entomologist hypothesizes that the mean life expectancy of a particular species of insect is 12.5 days. Researchers believing that the true mean is less than 12.5 days plan a hypothesis test at the 5% significance level on a random sample of 50 of these insects. If the alternative hypothesis is correct, for which of the following values of μ will the power of the test be greatest?
the method of selection
A simple random sample is defined by
[(0.25)(8.7)]/2.3
Can shoe size be predicted from height? In a random sample of 50 adults, the standard deviation in heights was 8.7 cm, while the standard deviation in shoe size was 2.3. The least squares regression equation was:
Predicted shoe size= -33.6 + 0.25(height in cm)
What was the correlation?
The researcher concludes he has evidence his new medication helps more than insulin injection, when in reality his medication is not better than insulin injection.
A researcher would like to show that a new oral diabetes medication he developed helps control blood sugar level better than insulin injection. He plans to run a hypothesis test at the 5% significance level.
What would be a Type I error?
The researcher concludes he has no evidence his new medication helps more than insulin injection, when in reality his medication is better than insulin injection.
A researcher would like to show that a new oral diabetes medication he developed helps control blood sugar level better than insulin injection. He plans to run a hypothesis test at the 5% significance level.
What would be a Type II Error?
0.226
A researcher would like to show that a new oral diabetes medication he developed helps control blood sugar level better than insulin injection. He plans to run a hypothesis test at the 5% significance level.
The researcher thinks he can improve his chances by running five such identical hypothesis tests, each using a different group of diabetic volunteers, hoping that at least one of the tests will show that his new oral diabetes medication helps control blood sugar level better than insulin injection. What is the probability of committing at least one Type I error?
It equals 1
A financial analyst determines the yearly research and development investments for 50 blue chip companies. She notes that the distribution is distinctly not bell-shaped. If the 50 dollar amounts are converted to z-scores, what can be said about the standard deviation of the 50 z-scores.
x̅= 3.5, σx̅= 0.986
Tossing a fair die has outcomes {1,2,3,4,5,6} with mean 3.5 and standard deviation 1.708. If a fair die is thrown three times, and the mean of the resulting triplet is calculated, the mean and standard deviation of the set of all possible such triplets is
An error was made in calculating the standard deviation.
A 40-question multiple-choice statistics exam is graded as number correct minus ¼ number incorrect, so scores can range from -10 to +40. Suppose the standard deviation for one class's results is reported to be -3.14. What is the proper conclusion?
Some other reason
Of the 423 seniors graduating this year from a city high school, 322 plan to go on to college. When the principal asks an AP student to calculate a 95% confidence interval for the proportion of this year's graduates who plan to go to college, the student says that this would be inappropriate. Why?
All of the above would lead to biased results.
An AP Statistics student in a large high school plans to survey his fellow students with regard to their preference between using a laptop or using an iPad. Which of the following survey methods would result in an unbiased result?
0.542
The mean combined SAT score for students in one state is 1758 with a standard deviation of 213 while for a second state the mean is 1725 with a standard deviation of 228. Assuming both distributions are approximately normal, what is the probability that a randomly selected student in the first state scores higher than a randomly selected student in the second state?
17.3 ± 2.262(2.3/√10)
In a random sample of 10 insects of a newly discovered species, an entomologist measures an average life expectancy of 17.3 days with a standard deviation of 2.3 days. Assuming all conditions for inference are met, what is a 95% confidence interval for the mean life expectancy for insects of this species?
1
A coin is weighted so that heads is twice as likely to occur as tails. The coin is flipped repeatedly until a tail occurs. Let X be the number of flips made. What is the most probable value for X?
Linear regression t-test
Suppose we are interested in determining whether or not a student's score on the AP Statistics Exam is a reasonable predictor of the student's GPA in the first year of college. Which of the following is the best statistical test?
[(0.55)(0.30)] / [(0.55)(0.30) + (0.45)(0.20)]
A campus has 55% male students. Suppose 30% of the male students pick basketball as their favorite sport compared to 20% of the females. If a randomly chosen student picks basketball as the student's favorite sport, what is the probability the student is male?
Mean, 298.75 K; standard deviation, 3.5 K
The kelvin is a unit of measurement for temperature; 0 K is absolute zero, the temperature at which all thermal motion ceases. Conversion from Fahrenheit to Kelvin is given by
K= 5/9 X (F-32) + 273. The average daily temperature in Monrovia, Liberia, is 78.35°F with a standard deviation of 6.3°F. If a scientist converts Monrovia daily temperatures to the Kelvin scale, what will be the new mean and standard deviation?
Design 1 is a completely randomized design, while Design 2 is a block design.
A cattle veterinarian is considering two experimental designs to compare two sources of bovine growth hormone, or BVH, to spur increased milk production in Guernsey cattle. Design 1 involves flipping a coin as each cow enters the stockade, and if heads, giving it BVH from bovine cadavers, and if tails, giving it BVH from engineered E. coli. Design 2 involves flipping a coin as each cow enters the stockade, and if heads, giving it BVH from bovine cadavers for a specified period of time and then switching to BVH from engineered E. coli for the same period of time, and if tails, the order is reversed. With both designs, daily milk production is noted. Which of the following is accurate.
to determine if there is a linear association between two numerical variables
The purpose of the linear regression t-test is
If the sample is random, the size of the population doesn't matter.
Which of the following is a true statement about sampling?
1
Suppose, in a study of mated pairs of soldier beetles, it is found that the measure of the elytron (hardened forewing) length is always 0.5 millimeters longer in the female. What is the correlation between elytron lengths of mated females and males?
_
I I_
I I I_
I I I I_
I I I I I_
(graph skewed strongly right)
The age distribution for a particular debilitating disease has a mean greater than the median. Which of the following graphs most likely illustrates this distribution?
3.8
Suppose we have a random variable X where the probability associated with the value k is (10 k) (0.38)^k(0.62)^(10-k) for k= 0, . . . , 10.
What is the mean of X?
It is likely that the true mean fastball speed of all varsity pitchers is within 3 mph of the sample mean fastball speed.
It is hypothesized that high school varsity pitchers throw fastballs at an average of 80 mph. A random sample of varsity pitchers are timed with radar guns resulting in a 95% confidence interval of (74.5, 80.5). Which of the following is a correct statement?
stratified sample
Should college athletes be required to give their coaches their Facebook IDs and passwords? A survey of student-athletes is to be taken. The statistician believes that Division I, II, III players may differ in their views, so she selects a random sample of athletes from each Division to survey. This is a
Assign "0" to 0 heads, "1,2,3" to 1 head, "4,5,6" to 2 heads, "7", to 3 heads, and ignore "8,9."
Which of the following use of a random number table would be appropriate to simulate tossing 3 fair coins and noting the number of heads?
the sample size should be the same
The population of the Greater Tokyo area is 34,400,000 and of Karachi is 17,200,000. A random sample of citizens is to be taken in each city, and confidence intervals for the mean age in each city will be calculated. Assuming roughly equal sample standard deviations, to obtain the same margin of error for each confidence interval,
10
The midhinge is defined to be the average of the first and third quartiles. If the midhinge is 20 and the interquartile range is also 20, what is the first quartile?
The larger the sample size, the closer the sample distribution is to a normal distribution.
Which of the following is an incorrect statement?
85%
For male Air Force cadets, the recommended fitness level with regard to the number of push-ups is 34. In a test whether or not current classes of recruits can meet this standard, a t-test of Ho: μ=34 against Ha: μ<34 gives a P-value of 0.068. Using this data, among the following, which is the largest level of confidence for a two-sided confidence interval that does not contain 34?
0.303
In American roulette there are 18 red pockets, 18 black pockets, and two green pockets (labeled 0 and 00). The ball is equally likely to land in any of the 38 pockets. What is the probability that a player ends up with a positive outcome, that is, makes money, after 50 equal bets on "red" (that is, for each of 50 spins of the wheel, the player wins or loses the specified identical dollar bet depending on whether or not the ball lands in a read or non-red pocket, respectively)?
The difference between the sample percentage and the population percentage is likely to be less than 6%.
In the USA TODAY/Gallup poll taken shorty after the game, 64% of respondents who described themselves as baseball fans said Major League Baseball should overturn the umpire's safe call that cost pitcher Armando Gallaraga a perfect game. The poll based on 470 respondents has a margin of error of 6%. Which of the following statements best describes what is meant by the 6% margin of error?
46
A university has 12,000 female students and 8,000 male students. Fifty percent of the women use the student gym and 40% of the men use the student gym. A random sample of 100 students is selected. What is the expected number of students in the sample who use the gym?
4,975
A manufacturer makes batteries and claims they have a shelf life of one year. The manufacturer contends that the batteries will function 99.5% of the time after sitting without use for one year. If the company's claims are true, what is the expected number of non-defective batteries in a random sample of 5,000 one-year-old batteries?
Choose plan II over plan I.
A certain library has 10,000 books. Two thousand of these books are nonfiction books and the rest are fiction. In order to estimate the total number of pages in their nonfiction books, two plans are proposed.
Plan I:
(a) Sample 50 books at random
(b) Estimate the mean number of pages per book in a confidence interval.
(c) Multiply both ends of the interval by 10,000 to get an interval estimate of the total.
Plan II:
(a) Identify the 2,000 nonfiction books.
(b) Sample 50 nonfiction books at random.
(c) Estimate the mean number of pages for nonfiction books in a confidence interval.
(d)Multiply both ends of the interval by 2,000 to get an interval estimate of the total.
On the basis of the information given, which o the following is the better method for estimating the total number of pages in nonfiction books in the library?
No, because road conditions are confounded with brand.
To check the effect of wet road conditions on automobile stopping distances, five economy-sized cars from automaker A and five economy-sized cars from automaker B are tested, The cars from automaker A are tested on a dry straightaway and asked to accelerate to 50 miles per hour before trying to bring the vehicle to a complete stop when it reaches a white line. The cars from automaker B are tested in the same design except that the track is hosed down with water before testing. The distance between the white line and where the car comes to a rest is measured for each car and the mean for the cars stopping on the dry road is measured against the mean for the cars stopping on the wet road. Is this a good experimental design?
H0: μ = $100
HA: μ < $100
A window manufacturer claims that its new seal-tight system will save homeowners in cold climates $100 a month during winter. A consumer group is skeptical of this claim and thinks that the manufacturer may be overstating the utility savings. If μ represents the true average savings for this new window system, which of the following gives the null and alternative hypothesis that the consumer group should test?
Stanley's salary is 1.25 standard deviations below the average salary of other accountants with his experience level.
Stanley's boss told him that he did not deserve a raise and was making a comparable amount to other accountants with his experience. So Stanley gathered some data and found that the standardized score (z-score) for his salary as compared to other accountants with the same level of experience is -1.25.
Which of the following is the best interpretation of this standardized score?
I, II, and III
Uncle Hugo's Electronics decided to see whether a local music CD section would be profitable at its 1,00 stores nationwide. It decided to set up local music displays at its 100 biggest locations. In this study, Uncle Hugo's marketing department found that sales of local artists showed a signification increase in the stores' monthly profits over the six months the study was conducted. Which of the following statements explains why it would not be appropriate to say that all of the stores should add a local music section?
I. The study only targeted Uncle Hugo's largest locations and there may not be as much good local music available in smaller locations.
II. The study only lasted six months, there could be increased interest in newly available music that dies down over time.
III. CDs are becoming outdated and, as people become more likely to purchase their music online, long-term profitability of committing more store space to CDs is questionable.
The mode and the mean are equal.
Which of the following is not a requirement for using the normal distribution?
Median
Before going to college, Chelsea wanted to see if she could get some pocket money by selling her old car online. She did a sample of the bid prices on 25 similar cars sold online in the past month. Later Chelsea realized that the lowest-priced car in the same was mistakenly recorded as half the price it was mistakenly recorded as half the price it was actually sold for. However, after correcting the error, the corrected price was still less than or equal to any other car price in her sample. Which of the following sample statistics must have remained the same after the correction was made?
0.216
A carnival game requires you to make three baskets in a row to win a prize. Andre is a basketball player who normally makes 80% of his shots, but because of the trick rim he estimates that he can only make the shot 60% of the time. What is the probability that Andre wins a prize if he decides to play the game once?
A motorist is in the country legally but does not have the paperwork to prove it in his or her vehicle.
Illegal immigration is an issue that many states are struggling to combat. A bill is put before Congress that would allow local police officers in border states to ask motorists to prove that they are U.S. citizens during routine traffic stops. If it is determined that these motorists are not in the United States legally, then they will be deported. Putting this in terms of a hypothesis test, H0 is that the motorist is in the United States legally and Ha is that the motorist is not in the United States legally. Which of the following is an example of a Type I error?
32.98 < μ < 36.42
A random sample of the number of people in a gym at noon produces a mean of 34.7 people and a standard deviation of 8.1 people. If the size of this sample is 60 days, which of the following is an approximate 90% confidence interval for the average number of people in the gym at noon?
Mr. Branch is correct.
Mr. Branch and his son Dennis both played on their college basketball teams. Mr. Branch scored 12.5 points per game at a time when the average player college scored 11 points a game with a standard deviation of 3.8 points. Dennis scores 15.8 points a game when the average player scores 14 points a game with a standard deviation of 6.1. Mr. Branch contends that while he'd proud of his son, he was a better scorer compared to the players of his day than his son is compared to his contemporaries. Dennis disagrees; he thinks his average is statistically better than his father's. Who is statistically correct in saying that he did better when compared to his peers?
Number the former client list. Use a table of random numbers to choose 50 clients from the master list and survey them.
An art gallery wants to conduct a survey to see what type of offerings people are most interested in. It wants to begin with a simple random sample of 50 people who have previously purchased art at the gallery. Which of the following survey methods will produce a simple random sample.
There is reason to conclude that μ > 23.
In a test of the null hypothesis H0: μ = 23 against the alternative hypothesis Ha: μ > 23, a sample from a normal population produces a mean of 28.9. The z-score for the sample is 2.48 and the P-value is 0.0066. based on these statistics, which of the following conclusions can be drawn?
281.6
There is a linear relationship between the amount of fat in a sandwich and the amount of calories in a sandwich. A least-squares fit of some data collected by a nutritionist gives the model
y = 217.3 + 35.2x
5 < x < 30
where x is the grams of fat in the sandwich and y is the estimated caloric content of the sandwich. What is the estimated increase in calories that corresponds to an increase of 8 grams of fat?
116
The costs of candy bars are approximately normally distributed about a mean of 90 cents with a standard deviation of 15 cents. If a Decadence Bar is in the 96th percentile for cost of candy bars, then its cost, in cents, is closest to
-0.31
The equation of the least-squares regression line for the points on the scatterplot below is y = 0.68 + 1.21x. What is residual for the point (3,4)?
0.0001
The process of packing candy corn yields bags with varying amounts of candy pieces. It is claimed that an average bag of candy corn contains 350 pieces. The Consumer's Corner magazine tests a random sample of 80 bags. The mean number of pieces of candy corn for this sample is 342.8, while the standard deviation is 12.4. What is the approximate P-value for the appropriate test.
19.2 < μ < 36.8
A survey was conducted to determine what percentage of California natives would rather live in a different state if they had a similar job to their current one. In a random sample of 100 Californian workers, 28% indicated that they would live in another state. A 95% confidence interval for the percentage of all Californian workers who would change states if they could is:
0.037
Sally realizes that all of her professors are going to give an exam of some kind in the half week that leads up to Thanksgiving break. If Sally takes four classes, and each class is equally likely to place its exam on either the Monday, Tuesday, or Wednesday before Thanksgiving break, what is the probability that Sally has all four of her exams on one day?
Name
Which of the following is not an effective example of a confounding variable within a study of the effect of stricter dieting leading to weight loss in pounds?
Outlier
While the periodic table provides an atomic mass for each element, these figures do not prove accurate for certain isotopes of some elements. Because these isotopes are likely to contain a different mix of neutrons and electrons, their weights are significantly more or less than the general element. The isotopes occur much more rarely than the general element, such that if you were to plot the weights of the element and its isotopes, the isotopes could be clearly identified as falling far away from the accepted mean. The best word to describe the isotopes as they relate to such a plot in statistics would be
90% of the time when a consumer buys peanut butter or jelly, they also buy the other.
Sales of jelly and peanut butter at a local store have a correlation of 0.9. Which is the best explanation of what this correlation means?
01, 10, 17
The 23 members of the math club decide to hold the "random awards" in which they use a random number table to award 1st, 2nd, and 3rd prizes. Each member is given a two-digit number from 01 to 23, then the prizes are drawn in reverse order with 3rd prize being the first number who appears in the random number table below:
92646 90110 79365 04891 39174 39823
Which numbered members of the math club won the three prizes?
72.4
If the test score average for a class of 30 students is 75.6 and the test score average for another class of 24 students is 68.4, what is the overall average for this test between the two classes?
9.375
The grades at a large school have an approximately normal distribution with a mean of 50. What standard deviation would be necessary to insure that 80% of the students are within 12 points above or below the mean?
0.63 ± 1.645 √[(0.63)(0.37)/150]
A SRS of 150 students at a local high school was taken to see how many like strawberry-flavored licorice. Ninety-five of the students liked strawberry licorice. What would be an appropriate set-up for a 90% confidence interval?
0.34
Amy is graduating in the spring from Howard University with a degree in accounting. AmeriGroup has offered her a job with a starting salary of $48,000 per year. Amy wants to know how may standard deviations below or above the mean is her starting salary if the mean and standard deviations for intro level accounting positions is $47,500 and 1470 respectively.
Not all Americans would have e-mail to respond.
An online survey was sent to every e-mail address in America. The online survey meant to determine how Americans feel about cigarette smoking in public places. What is wrong with the sampling method?
Nonresponse bias
A cell phone company wants to know how happy their customers are with their customers are with their service. The company sent a text message with a survey to every customer's phone. Out of the 100,000 customers 42,000 replied. Based on the 42,000 result they concluded the satisfaction level of their customers from the responses. What bias does this create?
0.74
The correlation between year of experience on a dental staff and the pay increase per year is found to be r=0.74. What will the correlation be if 2 years are added to all the values and the years of experience and pay increase were interchanged on the x and y axis?
The correlation between the amount of fertilizer and yield in potato crops was found to be r=0.58.
All but one of the following statements contain an error regarding bivariate data. Which of the following statements is correct?
Take one type of fabric first and number the 100 pieces 00-99. Using a random number table, pull out the first 50 two-digit numbers. These first 50 pieces would get the new retardant, the remaining 50 get old retardant. Repeat this process for the other fabric as well.
A new type of flame retardant created for clothing is ready for testing. There are two types of fabric that this retardant is to be tested on to see if it is better than the current substance used on these fabrics. How could an experiment be set up to study the effectiveness of this new retardant? There are 100 pieces of each type of fabric available for testing.
To keep the subject and person in contact with the subjects from influencing the variables.
Why is double-blind used in a study?
-$1.50
A lottery ticket is sold for $2 with the promise that someone will win this particular jackpot of $500. Only 1000 tickets are sold. What is the expected value of a ticket that was just purchased?
0.0605
Every year, 50% of all children will ask to stay home from school due to illness. What is the probability that 216 or more children out of a random sample of 400 will ask to stay home this year?
16-24
A standardized test is normally distributed with a mean of 20 and a standard deviation of 6. What would be the approximate interquartile range of the test scores?
I am 90% confident that the true height of newborns is contained in the interval.
A 90% confidence interval has been generated for the mean height in centimeters of newborn babies. What would the interval represent?
We are 98% confident that the true proportion of school age children who prefer morning recess outside is between 32% and 46%, based on this sample.
In a random sample of 300 school-age children in New York City schools, 39% said they preferred outside recess in the morning. If a 98% confidence interval were generated, what could be said about recess preferences of New York school children?
Yes, because the P=0.03, which is smaller than α.
A water consultant in a recently damaged region of the United States believes that the percentage of homes with contaminated water is higher than the recently reported 9%. The consultant surveyed 168 homes and found 23 homes with contaminated water. Is there enough evidence to reject the initial report of only 9% contamination at a α=0.05?
The sampling distribution of song lengths is approximately normal, population mean length is about 3.2 minutes and the population standard deviation is larger than 0.04.
In a study of 100 popular songs, the average length was found to be 3.2 minutes with a standard deviation of 0.04 minutes. Which of the following would be a true statement based on this study?
The process continues until a success occurs.
Which of the following is not a property of the binomial distribution?
x̅ ± 2.09 s/√20
Dequarius decides to take a simple random sample from a population that is normally distributed. However, the σ is not known. If his sample size is 20, and Dequarius wishes to generate a 95% confidence interval for the mean value, which formula would be correct?
It will decrease.
If Marvin has a simple random sample of 30 students, what will happen to the margin of error once he increases the sample size to 150?
μ=1000
A video game company is launching a test version of a new online game they are developing. Let μ be the mean number of players on the beta at one time. The company predicts that the more people who play the beta, the more successful the game will be when it is released. The number of players needed to predict the success of the game will be μ=1000. What would be the null hypothesis?
H0: p=0.39, H1: p<0.39
Congress claims that the proportion of people using public transportation is 0.39, which is good for the environment because there are fewer cars polluting the air. The environmental society disagrees, stating the proportion is far fewer. The society is in the process of conducting an experiment to support their disagreement. What would their hypothesis be?
Chi-square test of independence
A scientist wants to determine whether there is a relationship between gender and studying in high school students. What would be the best test to determine this?
Setting up a blind study where the administrator knows who is receiving which medication.
A researcher wants to study the effectiveness of two different medications for ADHD in children. One hundred children who are diagnosed with ADHD are randomly selected and half given each medication type. Which of the following could cause the introduction of the confounding variable?
μx̅= 7 and σx̅<2.24.
The population {4, 6, 8, 10} has mean μ=7 and standard deviation σ=2.24. If sampling is done with replacement, there are 16 different possible samples of size 2 that can be selected from this population. Each of these samples has a sample mean. For example, one of the samples is (8, 10), which has a mean of 9. Let the mean of the sampling distribution be denoted by μx̅ and the standard deviation by σx̅. Which of the following statements is true?
No, because a confounding variable of location within the store has been introduced.
A local store owner wants to know if a new line of souvenir glass figurines is a better sales product than a line he has carried for years. To test the two products, he decides to keep track of sales of each item for a period of one month. He randomly assigns one item to the checkout lane and the other to the second aisle in the store. If the new item is placed to the left of the checkout lane and the old item is randomly assigned to the second aisle, is this a good study?
Increasing the sample size
Which of the following will increase the power of a test?
Roughly 54% to 62% of the population who watch these shows would tend to prefer The Bachelor to Survivor.
A recent survey of reality show watchers found that 58% of the people preferred the reality show The Bachelor to the reality show Survivor with a margin of error of ±4%. What does this ±4% mean?
There is insufficient evidence that the slope of the regression line is not 0.
If a 95% confidence interval for the slope of a regression line were generated, what would it mean if the interval contained 0?
Yes. z=1.93, P=0.026
Americans say that being trimmer is very important to their self-image with 51% saying they would give up something to be thinner. A recent poll of 1001 adults said that 54% of them would give up watching television or shopping for the summer if they could be sure they would flatten their stomach. Is there evidence that Americans are becoming more weight conscious? Justify your response.
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