MC Quiz 1

In a US Today/Gallup poll taken shortly 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?

• About 6% of the baseball fans agreed with the umpire's call.

• About 6% of those polled were not actually baseball fans.

• The difference between the sample percentage and the population percentage is likely to be less than 6%.

• About 6% of the sample should not be included in the population.

• The difference between the percentage of people in favor of overturning the call in this survey and in a second similar survey would be less than 6%.

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 simple random sample of 100 students is selected. What is the expected number o students in the sample who use the gym?

• 47

• 46

• 45

• 44

• 43

A manufacturer of batteries claims they have a shelf life of one year. The manufacturer contends that 99.5% of the batteries will function after sitting without use for one year. If the company's claim is true, what is the expected number of batteries in a random sample of 5,000 one-year-old batteries that will function?

• 4,750

• 4,925

• 4,950

• 4,975

• 4,995

A fertilizer company is trying to convince corn farmers using a particular fertilizer that their new product CORNPLOSION will lead to an increase in yield over the currently used fertilizer. To determine which fertilizer results in a higher yield of corn, 10 one-acre fields are split into halves. The current fertilizer is used on one-half of each field and CORNPLOSION on the other half. The fertilizer that goes on the east half of the field is determined by a coin flip. The yield of the corn is measured in bushels per acre. What are the number of degrees of freedom associated with the appropriate t test for testing to see if there is a difference between the mean corn yield for the two types of fertilizer?

• 9

• 10

• 18

• 19

• 20

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: Sample 50 books at random. Estimate the mean number of pages per book using a confidence interval. Multiply both ends of the interval by 10,000 to get an interval estimate of the total.
Plan II: Identify the 2,000 nonfiction books. Sample 50 nonfiction books at random. Estimate the mean number of pages of nonfiction books using a confidence interval. 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 of the following is the better method for estimating the total number of pages in nonfiction books in the library?

• Choose plan I over plan II.

• Choose plan II over plan I.

• Choose either plan, since both are good and will produce equivalent results.

• Choose neither plan, since neither estimates the total number of nonfiction pages.

• The plans cannot be evaluated from the given information.

To check the effect of wet road conditions on automobile stopping distances, five economy-size cars from automaker A and five economy-size cars from automaker B are tested. The same driver is used to test all cars. The driver accelerates to 50 miles per hour and then brings the vehicle to a complete stop when it reaches a white line. The cars from automaker A are tested on a dry straightway. The cars from automaker B are tested on the same track, but the track is hosed down with water before testing. The distance between the white line and where the car comes to a stop is measured for each car and the mean for the cars stopping on the dry road is compared to the mean for the cars stopping on the wet road. Is this a good experimental design?

• No because the means are not proper statistics for comparison.

• No because more than 2 brans should be used.

• No because road conditions are confounded with brand.

• No because the experiment should not be limited to economy-sized cars.

• Yes

A window manufacturer claims that its new seal-tight system will save homeowners in cold climates $100 a month on average during the winter. A consumer group is skeptical of this claim and thinks the the manufacturer may be overstating the savings. If mu represents the true mean savings for this new window system, which of the following gives the null and alternative hypothesis that the consumer group should test?

• Ho: mu <= $100
  Ha: mu > $100

• Ho: mu = $100
  Ha: mu not= $100

• Ho: mu <$100
  Ha: mu >= $100

• Ho: mu = $100
  Ha: mu < $100

• Ho: mu = $100
  Ha: mu > $100

Stanley’s boss told him that he did not deserve a raise and that Stanley was making an amount similar to other accountants with his experience. Stanley gathered some data and found that the z-score fo his salary s compared to other accountants with the same level of experience is -1.25. Which of the following is the best interpretation of this z-score?

• Stanley makes 1.25% less than other accountants with his experience level.

• Stanley makes 1.25% more than other accountants with his experience level.

• Stanley makes $1.25 less per pay period than the average for accountants with his experience level.

• Stanley’s salary is 1.25 standard deviations above the mean salary of other accountants with his experience level.

• Stanley’s salary is 1.25 standard deviations below the mean salary of other accountants with his experience level.

Uncle Hugo’s Electronics decided to see whether a local music CD section would be profitable at its 1,000 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 sale of local artists were significantly greater in stores with the local music display. Which of the following statements explains why it would not be appropriate to recommend 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. Only 100 stores had a local display while 900 stores did not have a local display.
III. The sample consisted of more than 5% of the population.

• I only

• II only

• III only

• I and II only

• I, II, and III

. Every Wednesday Burgerville has a “discount deck day.” A customer who comes in with a child may choose to pick two cards from a standard deck of playing cards. If the two cards are the same number then the child’s junior burger is free with the purchase of a megaburger. IF the two cards are the same suit, the the child’s junior burger is half price with the purchase of a mega burger. The menu price for a junior burger is $2.00 and a megaburger is $4.00. Let X represent the amount paid by a customer with a child for a junior burger and a mega burger. The expected value of X is $5.65 and the standard deviation is $0.59. If a customer with a child picks form the discount deck and purchases both a junior burger and a megaburger every Wednesday for 12 consecutive weeks, what is the total amount that the customer would expect to pay for all of the burgers?

• $5.65

• $56.50

• $65.50

• $67.80

• $70.00

Every Wednesday Burgerville has a “discount deck day.” A customer who comes in with a child may choose to pick two cards from a standard deck of playing cards. If the two cards are the same number then the child’s junior burger is free with the purchase of a megaburger. IF the two cards are the same suit, the the child’s junior burger is half price with the purchase of a mega burger. The menu price for a junior burger is $2.00 and a megaburger is $4.00. Let X represent the amount paid by a customer with a child for a junior burger and a mega burger. The expected value of X is $5.65 and the standard deviation is $0.59. If a customer with a child picks from the discount deck every Wednesday and buys both a junior burger and a megaburger for 5 consecutive weeks, what is the standard deviation of the total amount paid for all of the burgers.

• $0.26

• $0.35

• $1.32

• $1.74

• $2.95

Which of the following is not a property of all normal distributions?
I. The distribution is symmetric
II. The distribution is centered at 0.
III. The median and the mean are equal.

• I only

• II only

• III only

• I and II only

• I, II, and III

Before going to college, Chelsea wanted to see if she could get some pocket money by selling her old car online. She selected 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 sample was mistakenly recorded as half the price it 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 sample statistics must have remained the same after the correction was made?

• Mean

• Median

• Mode

• Range

• Variance

A carnival games 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. Assuming that successive shots are independent, what is the probability that Andre wins a prize if he decides to play the game once?

• 0.2

• 0.216

• 0.4

• 0.512

• 0.6

Laws have been proposed in some border states that would allow police officers 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, Ho is that the motors is in the United States legally and Ha is that the motors is not in the United States legally. Which of the following is an example of a Type I error?

• A motoris is in the country legally but does not have the paperwork to prove it in his or her vehicle and so the motorist is thought to not be in the country legally.

• A motoris is not in the country legally but has counterfeit paperwork that fools the police and so the motorist is thought to be in the country.

• A motorist is not in the country legally but when stopped gets deported.

• A motoris is not in the country legally but never gets stopped by the police.

• A motorist is in the country legally and is not sopped by the police.

The number of people in a gym at noon on each of 60 randomly selected days produces a mean of 34.7 people and a standard deviation of 8.1 people. Which of the following is an approximate 90% confidence interval for the mean number of people in the gym at noon.

• (26.70, 42.70)

• (32.95, 36.45)

• (32.65, 36.75)

• (33.65, 35.75)

• (34.48, 34.92)

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 number o points scored by a player in college was 11 points a game and the standard deviation was 3.8 points. Dennis scored 15.8 points a game when the average number of points scored by a player in college was 14 points a game and the standard deviation was 6.1. Mr. Branch contends that while he's proud of his son, he was a better scorer compared to the players of his day than his son was compared to his contemporaries. Who is correct in saying that he did better when compared to his peers?

• Mr. Branch is correct

• Dennis is correct, they both did equally well.

• Neither is correct, they both did equally well.

• There is no basis for comparison, since they played in different eras for different teams.

• There is not enough information for comparison, because the number of players in each era is not known.

A die is rolled six times, and the number of times a 3 is rolled is counted. This procedure of six dice rolls i repeated 100 times and the results are summarized in a frequency distribution. Which of the frequency distributions below is most likely to contain the results from these 100 trials?

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?

• Survey the 50 most recent purchasers.

• Survey the 50 purchasers who have spent the most money at the gallery.

• Use random numbers to choose 10 people each who have purchased watercolors, sculptures, canvas, photographs, and mixed media.

• Hold a brunch for previous customers and put comment cards at 50 randomly assigned seats.

• Number a list of all people who have previously made a purchase. Use a table of random numbers to choose 50 people from this list and survey them.

There is a linear relationship between the amount of fat in a sandwich and the amount of calories in a sandwich. A least-squares regression line was fit using some data collected by a nutritionist, resulting in the line y-hat = 217.3 + 35.2x 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?

• 35.2

• 217.3

• 281.6

• 498.9

• 1738.4

In a test of the null hypothesis Ho: mu = 23 against the alternative Ha: mu > 23, a random sample form a normal population with a known standard deviation produces a mean of 28.9. The z statistic for the test is 2.48 and the p-value is 0.0066. Based on these statistics, which of the following conclusions could be drawn?

• There is convincing evidence that mu > 23

• Due to random fluctuation, 49.34% of the time a sample produces a mean larger than 23.

• 0.66% of the time, rejecting the alternative hypothesis is an error.

• 0.66% of the time, the mean is above 23.

• 99.34% of the time, the mean is below 23.

The weights of watermelons are approximately normally distributed about a mean of 90 ounces and a standard deviation of 15 ounces. If a watermelon is in the 96th percentile for weight, then tis weight, in ounces, is closes to?

• 26

• 105

• 116

• 126

• 262

Ten golf carts were selected at random from a country club to be outfitted with an engine modification designed to increase their maximum rate of speed. The time needed to complete 18 holes was recorded fora group using the upgraded golf carts and a group using golf carts that had not been modified. The difference in means for the time needed to complete 18 holes was 24 minutes. With mu1 denoting the mean time for unmodified cars and mu2 denoting the mean time for modified carts, a 95% confidence interval estimate of the true difference in mean time, mu1 - mu2 is (16, 32). Which of the following statements is correct decision based on this confidence interval?

• We can be confident that mu1 is around 16 and mu2 is around 32.

• The country club should not change to modified carts because we can be confident that mu1 is greater than mu2.

• The country club should change to modified carts because we can be confident that mu1 is greater than mu2.

• The country club should not change to modified carts because we can be confident that there is no difference between mu1 and mu2.

• The country club should convert the modified carts back to the original engines because we are not confident that the modified carts are better.

The equation of the least-squares regression line for a set of data is y-hat=0.68 + 1.21x. What is the residual for the point (3, 4)?

• -0.31

• -0.68

• -1.52

• -3.63

• -4.31

A random variable X has a normal distribution centered at 100. About 10% of the time, X takes on a value that is less than 80. What is the approximate value of the standard deviation of X?

• 10.0

• 12.2

• 15.6

• 20.0

• 40.0

The process of packaging candy corn yields bags with varying numbers of candy pieces. The candy manufacturer claims that, on average, bags of candy corn contain 350 pieces. The consumer's Corner magazine tests a random sample of 40 bags. The mean number of pieces of candy corn for this sample is 346.8, while the standard deviation is 12.4. Which of the following describes the approximate P-value for a test to determine if there is evidence that the mean number of candies per bag is less than the candy maker claims?

• P-value < 0.001

• 0.001 < P-value < 0.01

• 0.01 < P-value < 0.05

• 0.05 < P-value < 0.10

• P-value > 0.10

A survey was conducted to estimate the proportion of California workers who would rather live in a different state. In a random sample of 100 California workers, 28% indicated that they would rather live in another state. A 95% confidence interval for the proportion of all Californian workers who would rather live in another state is:

• (0.192, 0.368)

• (0.207, 0.353)

• (0.230, 0.330)

• (0.234, 0.326)

• (0.255, 0.305)

Which of the following represents a distribution where the mean is greater than the median?

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?

• 0

• 0.012

• 0.037

• 0.250

• 0.333

Which of the following is least likely to be a potential confounding variable in a study of the effect diet has on weight loss in pounds?

• Gender

• Beginning Weight

• Times spent exercising

• Name

• Time spent watching TV

The periodic table provides an atomic mass for each element, but these figures do not prove accurate for certain isotopes of some elements. Because isotopes are likely to contain a different mix of neutrons and electrons, the weights of some isotopes can be significantly more or less than the weight of the general element. Such isotopes occur more more rarely than the general element. 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 work to describe the isotopes as they relate to such a plot in statistics would be:

• outlier

• residual

• deviation

• quartile

• minimum

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 place 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 member who appears in the random number table below when the digits are read two at a time:

92646 90110 79365 04891 39174 39823

Which numbered members of the math club won the three prizes?

• 11, 04, 17

• 9, 2, 6

• 01, 10, 17

• 01, 11, 10

• 23, 17, 10

Sales of jelly (X) and sales of peanut butter (Y) at a local store are recorded weekly. The correlation between X and Y is 0.9. Which is the best explanation of what this correlation means?

• 90% of customers either buy peanut butter or jelly.

• 90% of the time when a customer buys peanut butter, they also buy the jelly.

• 90% of the variability in peanut butter sales can be explained by variability in jelly sales.

• 81% of the variability in peanut butter sales can be explained by the variability in jelly sales.

• 90% of the time when the price of peanut butter goes up, so does the price of jelly.