LET Reviewer for Gen Ed & Math Major: Probability & Statistics

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This has 50-item multiple-choice questions.

Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5. How do the two scores compare relative to their respective distributions?

1 point

They are both 1 standard deviation below their respective means.

They are both 2 standard deviations below their respective means.

They are both 1 standard deviation above their respective means.

The score of 40 is 2 standard deviations below its mean, while the score of 45 is only 1 standard deviation below its mean.

Clear selection

Which of the following is not a continuous variable?

1 point

time to solve a problem

temperature

height

number of children in a family

Clear selection

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 6.0 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the probability that the response time is between 3 and 7 minutes

1 point

0.2525

0.0228

0.7248

None

Clear selection

Normal distribution can have a mean that corresponds to a negative number.

1 point

True

False

Sometimes

Neither

Clear selection

If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt?

1 point

No, the test was conducted with a risk of a type I error.

Yes, if we reject the null that suggests that it is false beyond all doubt.

No, the test was conducted with a risk of a type II error.

Yes, the test was conducted with a risk of a type I error.

Clear selection

Consider two normal curves. If the first one has a larger mean than the second one, must it have a larger standard deviation as well?

1 point

No. The values of 𝜇 and 𝜎 are independent.

Yes. The values of 𝜇 and 𝜎 are independent.

No. As 𝜇 increases, 𝜎 will decrease.

Yes. As 𝜇 increases, 𝜎 must also increase.

Clear selection

True or false? Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating 𝜇 is the magnitude of the difference between x and 𝜇.

1 point

False. By definition, the margin of error is the magnitude of the difference between x and 𝜎.

True. By definition, the margin of error is the magnitude of the difference between x and 𝜎.

True. By definition, the margin of error is the magnitude of the difference between x and 𝜇.

False. By definition, the margin of error is the magnitude of the difference between x and 𝜇.

Clear selection

What is an alternate hypothesis?

1 point

A specific hypothesis where the claim is that the population parameter does not equal 0.

A specific hypothesis where the claim is that the population parameter is equal to 0.

Any hypothesis that differs from the original claim being made.

A working hypothesis making a claim about the population parameter in question.

Clear selection

One of the top paid female wrestlers is 28 years old. If her age is 0.55 standard deviations below the mean, and the standard deviation for female wrestler ages is 5.9 years, what is the average age for all female wrestlers? Assume that female wrestler ages can be modeled with a normal distribution.

1 point

not enough information is given

31.2

23.3

24.8

Clear selection

Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x?

1 point

No. The expected value can be a value different from the exact value of x.

Yes. The expected value must always be one of its possible values of x.

Yes. The expected value can never be a value from the exact value of x.

No. The expected value will never be one of its possible values of x.

Clear selection

On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss?

1 point

Yes, since the coin is fair.

No, each outcome is equally likely regardless of the previous outcome.

Yes, tails will always result on the second toss.

No, tails will never occur on the second toss.

Clear selection

What does a standard score measure?

1 point

the number of standard deviations a measurement is from the mean

the number of standard deviations a measurement is from the lowest value

the number of standard deviations a measurement is from the highest value

the number of standard deviations that are present under a normal curve

Clear selection

What is a null hypothesis?

1 point

A specific hypothesis where the claim is that the population parameter is equal to 0.

Any hypothesis that differs from the original claim being made.

A working hypothesis making a claim about the population parameter in question.

A specific hypothesis where the claim is that the population parameter does not equal 0.

Clear selection

Do the probabilities add up to 1? Should they add up to 1?

1 point

Yes, but they should not because these values do not cover the entire sample space.

Yes, because these values cover the entire sample space.

No, because these values do not cover the entire sample space.

No, but they should because these values cover the entire sample space.

Clear selection

Does a raw score less than the mean correspond to a positive or negative standard score? What about a raw score greater than the mean?

1 point

Raw scores less than the mean will have negative standard scores; raw scores above the mean will have positive standard scores.

Raw scores less than the mean will have positive standard scores; raw scores above the mean will have negative standard scores.

Raw scores below and above the mean will have negative standard scores.

Raw scores below and above the mean will have positive standard scores.

Clear selection

What does it mean to say that the trials of an experiment are independent?

1 point

One outcome is less likely to happen than the other outcomes

The outcome of one trial affects the probability of success on any other trial.

The outcome of one trial does not affect the probability of success on any other trial.

One outcome is more likely to happen than the other outcomes.

Clear selection

For a normal distribution, is it likely that a data value selected at random is more than 2 standard deviations above the mean?

1 point

No. This event happens only 16% of the time.

No. This event happens only .015% of the time.

No. This event happens only 2.5% of the time.

Yes. This event happens quite frequently.

Clear selection

Which of the statement(s) is/are correct? I. A disadvantage of a telephone interview compared to a face-to-face questionnaire is that people tend to be less patient. II. The cheapest way of collecting data is an online survey.

1 point

Statement II is correct, statement I is incorrect.

Statement I is correct, statement II is incorrect.

cBoth statements are incorrect.

Both statements are correct.

Clear selection

Name of the bias that can occur when not everybody from the population is included in the sample?

1 point

Under coverage

Sampling bias

Convenience sampling

Response bias

Clear selection

True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for 𝜇.

1 point

True. Different random samples may produce different x values, resulting in different confidence intervals.

False. Different random samples may produce different x values, resulting in different confidence intervals.

False. Different random samples may produce different x values, resulting in the same confidence intervals.

True. Different random samples will produce the same x values, resulting in the same confidence intervals.

Clear selection

Consider a Statistics class with 45 female students and 55 male students. Only 25 females passed a difficult midterm exam, whereas 30 males passed the same exam. What is the probability that a randomly chosen student passed the exam?

1 point

55%

25/45

45%

1/4

Clear selection

Consider two discrete probability distributions with the same sample space and the same expected value. Are the standard deviations of the two distributions necessarily equal?

1 point

No, the individual probabilities may differ in a way that produces the same expected value but a different standard deviation.

No, the standard deviations of two different discrete probability distributions are never equal.

Yes, because both distributions have the same expected value, they will have the same standard deviation as well.

Yes, because both distributions have the same sample space, they will have the same standard deviation as well.

Clear selection

For the past 20 years, the high temperature on April 15th has averaged 𝜇 = 62 degrees with a standard deviation of 𝜎 = 4. Last year, the high temperature was 72 degrees. Based on this information, which of the following best describes last year's temperature on April 15th?

1 point

There is not enough information to compare last year with the average.

above average, but it is impossible to describe how much above average

far above average

a little above average

Clear selection

True or false? A larger sample size produces a longer confidence interval for 𝜇.

1 point

True. As the sample size increases, the maximal error decreases, resulting in a longer confidence interval.

False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.

True. As the sample size increases, the maximal error increases, resulting in a longer confidence interval.

False. As the sample size increases, the maximal error increases, resulting in a shorter confidence interval.

Clear selection

For a population with 𝜇 = 80 and 𝜎 = 12, what is the z score corresponding to X = 92?

1 point

+12.00

+1.20

+1.00

+0.50

Clear selection

A sample space must be collectively exhaustive and mutually exclusive.

1 point

true

false

either

neither

Clear selection

What can you say if a sample distribution (very large sample size) is very different from the population distribution?

1 point

You have to do further research

The sample is biased and does not represent the population well

No issues and may proceed with the analysis

Population is biased

Clear selection

If car insurance rates for teenagers is approximately normally distributed with a standard deviation of $620 per year, find the mean insurance rate for teenagers if 10.56% of teenagers pay more than $3,000 annually for car insurance.

1 point

$2,225

$3,775

$2,935

$2,380

Clear selection

You received several complaints that a specific type of doll you sell, the DollX, is defective. You decided to test 5 out of the 50 DollX chains you have in stock to determine whether or not you should report the fault to the supplier. What is the population of interest in this study?

1 point

All dolls

All previously sold DollX

All DollX

The 5 selected DollX

Clear selection

Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent. What is the probability that all 4 children are male?

1 point

1/16

2/16

3/16

4/16

Clear selection

What does the random variable for a binomial experiment of n trials measure?

1 point

The random variable measures the standard deviation of n trials.

The random variable measures the number of failures out of n trials.

The random variable measures the number of successes out of n trials.

The random variable measures the mean of n trials.

Clear selection

Which of the following is a continuous variable?

1 point

number of traffic fatalities per year in the state of Florida

number of ships in Pearl Harbor on any given day

time required to drive from home to college on any given day

number of days someone lives

Clear selection

If two events are mutually exclusive, can they occur concurrently?

1 point

Yes. By definition, mutually exclusive events can occur together.

No. By definition, mutually exclusive events cannot occur together.

No. Two events will never occur concurrently.

Yes. Any two events can occur concurrently.

Clear selection

True or false? If the sample mean x of a random sample from an x distribution is relatively small, when the confidence level c is reduced, the confidence interval for 𝜇 becomes shorter.

1 point

False. As the level of confidence decreases, the maximal error of estimate increases.

True. As the level of confidence decreases, the maximal error of estimate decreases.

False. As the level of confidence decreases, the maximal error of estimate decreases.

True. As the level of confidence decreases, the maximal error of estimate increases.

Clear selection

In an experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.50; the probability of outcome B is 0.20; and the probability of outcome C is 0.30. Suppose there are 10 trials. Can we use the binomial experiment model to determine the probability of four outcomes of type A, five of type B, and one of type C?

1 point

Yes. Each outcome has a probability of success and failure.

Yes. A binomial probability model applies to three outcomes per trial.

No. A binomial probability model applies to only one outcome per trial.

No. A binomial probability model applies to only two outcomes per trial.

Clear selection

If we fail to reject (i.e., "accept") the null hypothesis, does this mean that we have proved it to be true beyond all doubt?

1 point

Yes, if we fail to reject the null, we have found evidence that the null is true beyond all doubt.

No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis.

No, it suggests that the null hypothesis is true only some of the time.

Yes, it suggests that the evidence is sufficient to merit rejecting the alternative hypothesis beyond all doubt.

Clear selection

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 58 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean 𝜇 = 58 tons and standard deviation 𝜎 = 1 ton. Suppose the weight of coal in 45 cars selected at random had an average x of less than 57.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

1 point

Yes, the probability that this deviation is random is very small.

Yes, the probability that this deviation is random is very large.

No, the probability that this deviation is random is very small.

No, the probability that this deviation is random is very large.

Clear selection

Suppose you would like to estimate the proportion of the satisfied customer. Which of the following would be the best point estimate to use?

1 point

The number of satisfied customers out of a random sample of 100 customers

The proportion of satisfied customers out of a random sample of 100 customers

The proportion of satisfied customers out of the latest 100 customers to contact customer services

The average customer satisfaction rating given by a random sample of 100 customers

Clear selection

What is the difference between descriptive and inferential statistics?

1 point

Inferential statistics only concerns the sample while descriptive statistics concerns the underlying population

Descriptive statistics is used with discrete variables, inferential statistics is used with continuous variables.

Inferential statistics is used with discrete variables, descriptive statistics is used with continuous variables.

Descriptive statistics only concerns the sample, inferential statistics concerns the underlying population.

Clear selection

True or false? If the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for 𝜇 will be relatively short.

1 point

True. The maximal error of estimate controls the length of the confidence interval dependent on the value of x.

False. The maximal error of estimate controls the length of the confidence interval regardless of the value of x.

True. The maximal error of estimate controls the length of the confidence interval regardless of the value of x.

False. The maximal error of estimate controls the length of the confidence interval dependent on the value of x.

Clear selection

Raul received a score of 78 on a history test for which the class mean was 70 with a standard deviation of 8. He received a score of 74 on a biology test for which the class mean was 70 with standard deviation 4. On which test did he do better relative to the rest of the class?

1 point

biology test

history test

the same

none

Clear selection

As the degrees of freedom increase, what distribution does the student’s t distribution become more like?

1 point

chi-square

inomial

uniform

standard normal

Clear selection

Discrete random variables arise from measurement.

1 point

ture

false

either

neither

Clear selection

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean 𝜇 = 7100 and estimated standard deviation 𝜎 = 2850. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. What is the probability that, on a single test, x is less than 3500?

1 point

0.1033

0.1133

0.1233

0.1333

Clear selection

Real limits are important whenever you are measuring a(n) _____ variable.

1 point

independent

dependent

discrete

continuous

Clear selection

You flip a fair coin (i.e., the probability of obtaining Heads is 1/2) three times. Assume that all sequences of coin flip results, of length 3, are equally likely. Determine the probability of any sequence in which the number of Heads is greater than or equal to the number of Tails.

1 point

1/2

3/8

3/16

Clear selection

A z-score of z = −2.00 indicates a position in a distribution __________.

1 point

below the mean by 2 points

above the mean by a distance equal to 2 standard deviations

below the mean by a distance equal to 2 standard deviations

above the mean by 2 points

Clear selection

What is the central limit theorem?

1 point

It says that the sampling distribution forms a bell shape given that the sample is large enough and the population distribution is bell shaped.

It says that the mean is centered if the sample size is infinity.

It says that the sampling distribution forms a bell shape given that the sample is large enough.

It says that the population distribution approximates a bell shape given that the sample is large enough.

Clear selection

For a distribution of scores, which of the following z-score values represents the location closest to the mean?

1 point

z = −2.00

z = −1.00

z = +0.50

z = +1.00

Clear selection

1 point

All dolls

All previously sold DollX

All DollX

The 5 selected DollX

Clear selection

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