Statistics Trivia Questions for Students

A set consists of four numbers. The largest value is 200, and the range is 50. Which of the following statements is true?

• AThe mean is greater than 165.
• BThe mean is less than 185.
• CThe median is less than 195.
• DThe median is the mean of the second and third numbers if the set is arranged in ascending order.

A medicine is known to produce side effects in one in five patients taking it. Suppose a doctor prescribes the medicine to four unrelated patients. What is the probability that none of the patients will develop side effects?

• A0.8
• B0.2
• C0.25
• D0.4096

A simple random sample is defined by

• Aexamination of the outcome.
• Bhow representative the sample is of the population.
• Cboth of the above.
• Dthe method of selection.

A town has one high school, which buses students from urban, suburban, and rural communities. Which of the following samples is recommended in studying attitudes toward tracking of students in honors, regular, and below-grade classes?

• ASimple random sample (SRS)
• BStratified sample
• CSystematic sample
• DConvenience sample

The number of leasable square feet of office space available in a city on any given day has a normal distribution with mean 640,000 square feet and standard deviation 18,000 square feet. What is the interquartile range for this distribution?

• A652,000 - 628,000
• B658,000 - 622,000
• C676,000 - 604,000
• D667,000 - 613,000

The probability is 0.2 that a value selected at random from a normal distribution with mean 600 and standard deviation 15 will be above what number?

• A603.8
• B587.4
• C612.6
• D0.84

Define a new measurement as the difference between the 60th and 40th percentile scores in a population. This measurement will give information concerning

• Askewness.
• Bvariability.
• Ccentral tendency.
• Dsymmetry.

Suppose X and Y are random variables with μx = 32, σx = 5, μy = 44, and σy = 12. Given that X and Y are independent, what are the mean and standard deviation of the random variable X + Y?

• Aμx+y = 76, σx+y = 8.5
• Bμx+y = 76, σx+y = 13
• Cμx+y = 76, σx+y = 17
• Dμx+y = 38, σx+y = 17

The relation between studying time (in hours) and grade on a final exam (0-100) in a random sample of students in math class was found to be Grade = 50.25 + 10.2 (h) How will a student's grade be affected if she studies for two hours?

• AHer grade will remain unchanged.
• BHer grade will down by 10.2 points.
• CHer grade will go up by 40.05 points.
• DHer grade will go up by 20.4 points.

What is a sampling distribution?

• AA histogram, or other such visual representation, showing the distribution of a sample
• BA distribution of all the values taken by a statistic from all possible samples of a given size
• CA distribution of all the statistics that can be found in a given sample
• DA normal distribution of some statistic

The main purpose of blocking in an experiment is to:

• Areduce variation between treatments.
• Breduce confounding.
• Creduce bias.
• Dreduce variation within treatments.

Which of these is a correct description of the term?

• ALevels are the same as treatments.
• BA factor is a response variable.
• CExperimental units are the same as subjects.
• DReplication means the experiment should be repeated several times.

A local school has seven math teachers and seven English teachers. When comparing their mean salaries, which of the following is most appropriate?

• AA one-sample z-test on a set of differences
• BA two-sample z-test of population means
• CNone of the above are appropriate.
• DA two-sample t-test of population means

An outlier is an observation that

• Ais seen less frequently than the other observations in the data set
• Bis always smaller than the other observations in the data set
• Cis seen more frequently than the other observations in the data set
• Dis significantly different from the other observations in the data set

According to the central limit theorem, the sample mean X is approximately normally distributed

• Afor a small sample, regardless of the distribution of random variable X
• Bregardless of the sample size
• Cfor a large sample, provided the random variable X is normally distributed
• Dfor a large sample, regardless of the distribution of random variable X

In one metropolitan region, technical writers have an annual salary that is approximately normally distributed with a mean of $55,800. The first quartile of salaries is $48,815. What is the standard deviation?

• A$6,984
• B$13,968
• C$10,476
• D$10,356

Given that P(E) = 0.32, P(F) = 0.15, and P(E ∩ F) = 0.048, which of the following is a correct conclusion?

• AThe events E and F are both independent and mutually exclusive.
• BThe events E and F are mutually exclusive but not independent.
• CThe events E and F are independent but not mutually exclusive.
• DThe events E and F are neither independent nor mutually exclusive.

Which of the following is not important in the design of experiments?

• ARandomization in assigning subjects to different treatments
• BReplication of the experiment using sufficient numbers of subjects
• CControl of confounding variables
• DUse of a confounding variable to control the placebo effect

A telephone survey of 400 registered voters showed that 256 had not yet made up their minds 1 month before the election. How sure can we be that between 60% and 68% of the electorate were still undecided at that time?

• A64.0%
• B8.0%
• C90.4%
• D2.4%

For the regression line, which of the following statements about residuals is true?

• AInfluential scores have large residuals.
• BIf the correlation is 0, there will be a distinct pattern in the residual plot.
• CIf the linear model is good, the number of positive residuals will be the same as the number of negative residuals.
• DThe mean of the residuals is always zero.

Which of the following is least likely to reduce bias in a sample survey?

• AAsking questions in a neutral manner to avoid influencing the responses
• BUsing stratified random sampling rather than simple random sampling
• CSelecting samples randomly
• DFollowing up with those who did not respond to the survey the first time

Two dice are rolled simultaneously. If both dice show 6, then the player wins $20; otherwise the player loses the game. It costs $2.00 to play the game. What is the expected gain or loss per game?

• AThe player will lose about $1.44.
• BThe player will gain about $0.55.
• CThe player will gain about $1.44.
• DThe player will lose about $0.55.

Random variable X is normally distributed, with a mean of 25 and a standard deviation of 4. Which of the following is the approximate interquartile range for this distribution?

• A27.70 – 22.30 = 5.40
• B2.00(4.00) = 8.00
• C27.70 ÷ 22.30 = 1.24
• D25.00 – 22.30 = 2.70

If all the values of a data set are the same, all of the following must equal zero except for which one?

• ARange
• BStandard deviation
• CMean
• DVariance

The sampling distribution of the sample mean is close to the normal distribution

• Aif n is large, no matter what the distribution of the original population.
• Bno matter what the value of n or what the distribution of the original population.
• Cif the standard deviation of the original population is known.
• Donly if both the original population has a normal distribution and n is large.

For which of these is a binomial probability model most reasonable?

• AThe number of times, out of 10 attempts, that a particular child can throw a ball into a basket from six feet away
• BThe number of cards drawn from a well-shuffled deck until all four aces are found
• CThe number of times that a randomly selected resident of California has visited a museum in the last 12 months
• DThe colors of the cars in the parking lot of a particular grocery store on a randomly selected Sunday

Suppose you wish to compare the AP Statistics exam results for the male and female students taking AP Statistics at your high school. Which is the most appropriate technique for gathering the needed data?

• ACensus
• BExperiment
• CObservational study
• DSample survey

A particular crop of one variety of onion has weights that are approximately normally distributed with mean 9.8 oz. and standard deviation 2.1 oz. How does an onion in the 28th percentile for weight compare to the mean?

• A1.22 ounces below the mean
• B1.22 ounces above the mean
• C0.59 ounces above the mean
• D0.59 ounces below the mean

The distribution of weights of 16-ounce bags of a particular brand of potato chips is approximately normal with a standard deviation of 0.28 ounce. How does the weight of a bag at the 40th percentile compare with the mean weight?

• A0.40 ounce above the mean
• B0.07 ounce above the mean
• C0.25 ounce above the mean
• D0.07 ounce below the mean

Which of the following is true about any discrete probability distribution of a random variable X?

• AThe probability distribution is bell-shaped and symmetric.
• BThe probabilities of all possible values of X must add up to one.
• CThe expected value of X = np.
• DThe sum of all possible values of X is equal to one.

Which of the following is NOT true of the χ2 probability distribution function?

• AFor the same α, as the number of degrees of freedom increases, the critical value for the rejection region decreases.
• BThe area under the χ2 curve is 1.
• Cχ2 is defined only for nonnegative values of the variable.
• DFor small degrees of freedom, the curve displays strong right-skewness.

Suppose X and Y are random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and var(Y) = 12. What are the expected value and variance of the random variable X + Y?

• AE(X + Y) = 99, var(X + Y) = 17
• BE(X + Y) = 99, var(X + Y) = 13
• CThere is insufficient information to answer this question.
• DE(X + Y) = 99, var(X + Y) = 8.5

In which of the following situations is a binomial model not an appropriate model to describe the outcome?

• AThe number of students present in a class of 22
• BThe number of heads in three tosses of a coin
• CThe number of rainy days in a given week
• DThe number of girls in a family of five children

A sample of size 35 is to be drawn from a large population. The sampling technique is such that every possible sample of size 35 that could be drawn from the population is equally likely. What name is given to this type of sample?

• ACluster sample
• BVoluntary response sample
• CSystematic sample
• DSimple random sample

A correlation of 0.6 indicates that the percentage of variation in y that is explained by the variation in x is how many times the percentage indicated by a correlation of 0.3?

• A2
• B4
• C6
• D3

Two events A and B each have a nonzero probability. If A and B are independent, which of the following statements is true?

• AA and B may or may not be mutually exclusive.
• BA and B must be mutually exclusive.
• CP(A and B) = P(A) · P(B)
• DP(A| B) = P(B| A)

In a group of 10 scores, the largest score is increased by 40 points. What will happen to the mean?

• AIt will increase by 10 points.
• BIt will remain the same.
• CIt will increase by 4 points.
• DIt will increase by 40 points.

A hypothesis test is set up so that P(rejecting H0 when H0 is true) = 0.05 and P(failing to reject H0 when H0 is false) = 0.26. What is the power of the test?

• A0.05
• B0.74
• C0.95
• D0.26

Which of the following is notrequired in a binomial setting?

• AThe value of the random variable of interest is the number of trials until the first success occurs.
• BThere is a fixed number of trials.
• CEach trial is considered either a success or a failure.
• DEach trial is independent.

Consider a hypothesis test with H0 : μ = 70 and Ha : μ < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when μ = 65?

• Aα = 0.05, n = 30
• Bα = 0.01, n = 15
• Cα = 0.01, n = 30
• Dα = 0.05, n = 15

Two classes take the same exam. Suppose a certain score is at the 40th percentile for the first class and at the 80th percentile for the second class. Which of the following is the most reasonable conclusion?

• AA score at the 50th percentile for the first class is at the 90th percentile for the second class.
• BStudents in the second class generally scored higher than students in the first class.
• CStudents in the first class generally scored higher than students in the second class.
• DA score at the 20th percentile for the first class is at the 40th percentile for the second class.

What are the mean and standard deviation of a binomial experiment that occurs with probability of success 0.76 and is repeated 150 times?

• A100.5, 5.23
• BThe mean is 114, but there is not enough information given to determine the standard deviation.
• C114, 27.35
• D114, 5.23

Jonathan obtained a score of 80 on a statistics exam, placing him at the 90th percentile. Suppose five points are added to everyone's score. Jonathan's new score will be at the

• A85th percentile.
• B80th percentile.
• C95th percentile.
• D90th percentile.

Which of the following is not true about t-distributions?

• At-distributions always have mean 0 and standard deviation 1.
• BThere are different t-distributions for different values of df (degrees of freedom).
• Ct-distributions are more spread out than the normal distribution.
• Dt-distributions are bell-shaped and symmetric.

A high school sent a survey to a randomly selected sample of 75 of last year's graduating class. 27 of those selected did not return the survey. The best plan of action would be to:

• AUse the surveys that were returned and change the sample size to 48 for the analysis.
• BUse the surveys that were returned and leave the sample size at 75 for the analysis.
• CFollow up with those that did not return the survey to encourage them to respond.
• DRandomly select 27 additional class members and send the survey to them.

Which of the following statements about any two events A and B is true?

• AP(A ∩ B) = 0 implies events A and B are mutually exclusive.
• BP(A ∪ B) = 1 implies events A and B are mutually exclusive.
• CP(A ∩ B) = 0 implies events A and B are independent.
• DP(A ∪ B) implies events A and B are independent.

The number of customers served per day by a large department store is normally distributed, with a mean of 3,250 customers and a standard deviation of 320. Find the range of customers served on the middle 50 percent of days.

• A(3,034, 3,466)
• B(2,610, 3,890)
• C(2,930, 3,570)
• D(2,450, 4,050)

Two variables, xand y, seem to be exponentially related. The natural logarithm of each yvalue is taken and the least-squares regression line of ln(y) on xis determined to be ln(y) = 3.2 + 0.42x. What is the predicted value of ywhen x= 7?

• A464.05
• B521.35
• C1380384.27
• D6.14

As reported on CNN, in a May 1999 national poll 43% of high school students expressed fear about going to school. Which of the following best describes what is meant by the poll having a margin of error of 5%?

• AFive percent of the students refused to participate in the poll.
• BBetween 38% and 48% of those surveyed expressed fear about going to school.
• CThere is a 0.05 probability that the 43% result is in error.
• DIt is likely that the true proportion of high school students afraid to go to school is between 38% and 48%.

A one-sided test of a hypothesis about a population mean, based on a sample of size 14, yields a P-value of 0.075. Which of the following best describes the range of tvalues that would have given this P-value?

• A1.345 < t< 1.761
• B1.350 < t< 1.771
• C1.771 < t< 2.160
• D1.356 < t< 1.782