Statistics Trivia Questions for Students — page 2

The director of a local food bank asks for data on all donations given during the month of November. Of the 100 checks received, the average donation is $155 with a standard deviation of $32. Which of the following is the most appropriate statement?

• AThis November, the average donation is $155.
• B50% of all donations this November are more than $155.
• CWe are 95% confident that the average donation in November is between about $149 and $161.
• DWe are 95% confident that the average donation in November is between about $91 and $219.

Given that the sample has a standard deviation of zero, which of the following is a true statement?

• AThe standard deviation of the population is also zero.
• BThe sample mean and sample median are equal.
• CThe sample may have outliers.
• DThe population has a symmetric distribution.

Assume that the masses of chicken eggs are normally distributed with a mean of 45 g and a standard deviation of 4 g. What mass of egg would be the 25th percentile of the masses of all the eggs?

• A42.5 g
• B42.2 g
• C42.3 g
• D42.4 g

Given the probabilities P(A) = 0.3 and P(B) = 0.2, what is the probability of the union P(A ∪ B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A?

• A.5, 0.44, 0.2
• B.44, 0.5, 0.3
• C0.44, 0.5, 0.2
• D.5, 0.44, 0.3

In general, how does tripling the sample size change the confidence interval size?

• AIt triples the interval size.
• BIt multiples the interval size by 1.732.
• CIt divides the interval size by 1.732.
• DIt divides the interval size by 3.

In the correlation coefficient r = 0.78, what percentage of variation in y is explained by the linear regression model?

• A39%
• B61%
• C44%
• D22%

The observed times (in minutes) it takes a runner to complete a marathon are normally distributed. The z-score for his running time this week is –2. Which one of the following statements is a correct interpretation of his z-score?

• AThis week his time was two minutes lower than his best time ever.
• BThis week his time was two minutes lower than his time last week.
• CThis week his time was two minutes lower than his average time.
• DThis week his time was two standard deviations lower than his average time.

In sample surveys, what is meant by bias?

• ATendency for some distributions to be skewed.
• BA systematic error in a sampling method that leads to an unrepresentative sample.
• CNatural variability seen between samples.
• DPrejudice, as in ethnic and gender-related studies.

Sampling error occurs

• Awhen interviewers use judgment instead of random choice in picking the sample.
• Bbecause a sample statistic is used to estimate a population parameter.
• Cwhen samples are too small.
• Dwhen interviewers make mistakes resulting in bias.

The average number of calories in Yum-Yum Good candy bars is 210, with a standard deviation of 10. If the number of calories per candy bar is normally distributed, what percent of candy bars contain more than 225 calories?

• A47.70%
• B66.80%
• C6.68%
• D43.30%

Which of the following is a false statement about simple random samples?

• AA sample must be reasonably large to be properly considered a simple random sample.
• BAttributes of a simple random sample may be very different from attributes of the population.
• CInspection of a sample will give no indication of whether or not it is a simple random sample.
• DEvery element of the population has an equal chance of being picked.

Suppose there is a correlation of r = 0.9 between number of hours per day students study and GPAs. Which of the following is a reasonable conclusion?

• A90% of students who study receive high grades.
• B90% of students who receive high grades study a lot.
• C90% of the variation in GPAs can be explained by variation in number of study hours per day.
• D81% of the variation in GPAs can be explained by variation in number of study hours per day.

A chi-squared test of independence is to be performed on a 3 × 4 contingency table. How many degrees of freedom does this test have?

• A8
• B11
• C10
• D6

Consider the two sets X = {10, 30, 45, 50, 55, 70, 90} and Y = {10, 30, 35, 50, 65, 70, 90}. Which of the following is false?

• AThe sets have identical ranges.
• BThe sets have identical medians.
• CThe sets have identical means.
• DNone of the above are false.

We are interested in the proportion p of people who are unemployed in a large city. Eight percent of a simple random sample of 500 people are unemployed. What is the midpoint for a 95% confidence interval estimate of p?

• A0.012
• B0.475
• CNone of the above.
• D0.025

You need to construct a 94% confidence interval for a population proportion. What is the upper critical value of z to be used in constructing this interval?

• A1.555
• B1.88
• C0.9699
• D1.96

The number of days it takes to build a new house has a variance of 386. A sample of 40 new homes shows an average building time of 83 days. With what confidence can we assert that the average building time for a new house is between 80 and 90 days?

• A15.4%
• B17.8%
• C20.0%
• D82.1%

Changing from a 90% confidence interval estimate for a population proportion to a 99% confidence interval estimate, with all other things being equal,

• Adecreases the interval size by 9%.
• Bincreases the interval size by 57%.
• Cdecreases the interval size by 57%.
• Dincreases the interval size by 9%.

Which of these statements correctly explains bias?

• AIt describes a lack of randomization in the sampling process.
• BIt describes a process that creates estimates that are too high on average or too low on average.
• CIt describes a sample that is not representative of the population.
• DIt describes a process that results in a sample that does not represent the population.

A 2008 survey of 500 households concluded that 82% of the population uses grocery coupons. Which of the following best describes what is meant by the poll having a margin of error of 3%?

• AThree percent of those surveyed refused to participate in the poll.
• BIt would not be unexpected for 3% of the population to begin using coupons or stop using coupons.
• CIt is likely that between 79% and 85% of the population use grocery coupons.
• DBetween 395 and 425 of the 500 households surveyed responded that they used grocery coupons.

Which of the following is most useful in establishing cause-and-effect relationships?

• AA least squares regression line showing high correlation
• BA complete census
• CAn experiment
• DA simple random sample (SRS)

Which of the following statements about the correlation coefficient is true?

• AThe correlation coefficient and the slope of the regression line may have opposite signs.
• BA correlation of 1 indicates a perfect cause-and-effect relationship between the variables.
• CCorrelation applies equally well to quantitative and categorical data.
• DCorrelations of +0.87 and -0.87 indicate the same degree of clustering around the regression line.

The binomial distribution is an appropriate model for which of the following?

• AThe number of drivers wearing seat belts if 10 consecutive drivers are stopped at a police roadblock.
• BThe number of minutes in an hour for which the Dow-Jones average is above its beginning average for the day.
• CThe number of cities among the 10 largest in New York State for which the weather is cloudy for most of a given day.
• DNone of the above.

Suppose you did 10 independent tests of the form H0: μ = 25 versus Ha: μ < 25, each at the α = 0.05 significance level. What is the probability of committing a Type I error and incorrectly rejecting a true H0 with at least one of the 10 tests?

• A0.50
• B0.40
• C0.05
• D0.60

A significance test of the hypothesis H0: p= 0.3 against the alternative HA: p> 0.3 found a value of = 0.35 for a random sample of size 95. What is the P-value of this test?

• A0.2275
• B1.06
• C0.1446
• D0.8554

On the same test, Mary and Pam scored at the 64th and 56th percentiles, respectively. Which of the following is a true statement?

• AMary's score is 8% higher than Pam's.
• BEight percent of those who took the test scored between Pam and Mary.
• CThirty-six people scored higher than both Mary and Pam.
• DMary scored eight more points than Pam.

Which of the following can affect the value of the correlation r?

• ANone of the above can affect the r value.
• BA change in measurement units
• CA change in which variable is called x and which is called y
• DAdding the same constant to all values of the x-variable

Suppose that 60% of a particular electronic part last over 3 years, while 70% last less than 6 years. Assuming a normal distribution, what are the mean and standard deviation with regard to length of life of these parts?

• Aμ = 3.977, σ = 3.861
• Bμ = 4.377, σ = 3.261
• Cμ = 3.677, σ = 3.561
• Dμ = 4.177, σ = 3.561

Which among the following would result in the narrowest confidence interval?

• ALarge sample size and 95% confidence
• BSmall sample size and 95% confidence
• CLarge sample size and 99% confidence
• DSmall sample size and 99% confidence

Suppose X and Y are random variables with E(X) = 312, var(X) = 6, E(X) = 307, and var(Y) = 8. What are the expected value and variance of the random variable X + Y?

• AE(X + Y) = 619, var(X + Y) = 14
• BE(X + Y) = 619, var(X + Y) = 7
• CE(X + Y) = 619, var(X + Y) = 10
• DThere is insufficient information to answer this question.