Stats Exam 1

Even though the length of phone calls to the Boston mayor's office (in one of the videos) were not normally distributed (most calls were very short but a few were quite long), the sampling distribution of the sample mean time of calls 𝑥⎯⎯⎯x¯ was approximately normally distributed when the sample size 𝑛n was large. Select one: True False

True

In terms of batting average and home runs, Joe Mauer generally did better in his early years with the Minnesota Twins than in his later years. Select one: True False

True

Parameters describe populations and statistics are computed from samples. Select one: True False

True

The distinction between explanatory and response variables is not essential for the correlation r. The formula is symmetric in x and y. Select one: True False

True

The distinction between two quantitative variables x and y is essential for regression. The formulas are not symmetric in x and y. Select one: True False

True

The list of prerequisites for success that I emphasized were: desire, commitment, time management, and grit. Select one: True False

True

The notation 𝑃(𝐴 | 𝐵)P(A | B) represents the conditional probability of A occurring, given that we know B has occurred. Select one: True False

True

The quantity 𝑧=(𝑥−𝜇)/𝜎 tells us how many standard deviations x is above or below the mean 𝜇. Select one: True False

True

The slope of a line measures the rate of change of y with respect to x along the line. Select one: True False

True

The squared correlation 𝑟^2 (called the coefficient of determination) is a better measure of the strength of a linear relationship between 𝑥x and 𝑦y than the correlation 𝑟r is. Select one: True False

True

When a percentage goes up from, for example, 4% to 4.05% percent, we say it has gone up by 0.05 percentage points. Select one: True False

True

When coral reefs were studied to see the impact of humans, it was an example of an observational study. Select one: True False

True

When x changes by one of its standard deviations, then y changes by r of its standard deviations. Select one: True False

True

The "shortcut" formula for 𝑆𝑆𝑥𝑥 is

=∑x^2−(∑x)^2n.

If the regression line for a data set is 𝑦(hat)=5+3𝑥, and one data point is (𝑥,𝑦)=(4,15), then the residual for that data point is Select one: a. -2 b. 2 c. 17 d. 3

A - -2

Use Table A or your calculator to find the area under the standard Normal curve N(0,1) between z = -0.41 and z = 0.98. Select one: a. .4956 b. .5017 c. .8365 d. .4894

A - .4956

Use Table A or your calculator to find the area under the standard Normal curve N(0,1) between z = -0.41 and z = 0.98. Select one: a. .4956 b. .8365 c. .5017 d. .4894

A - .4956

What is the probability of getting 3 heads in a row when you toss a fair coin 3 times? (Note: heads and tails are equally likely on each individual toss). Select one: a. 1/8 b. 1/2 c. 1/16 d. 1/4

A - 1/8

A statistics exam has a mean score of 82 points and a standard deviation of 8 points. To the nearest whole number, find the exam score at the 60th percentile. Select one: a. 84 b. 88 c. 60 d. 86

A - 84

Why is the least squares line also called a regression line? Select one: a. Because Sir Francis Galton observed that, when fathers were above average in height, so were their sons, though not as much. b. Because Sir Alec Guinness tried to see to it that Luke would not regress by knowing who his father was. c. Because Sir Paul McCartney thought that John was being retrograde in dating Yoko. d. Because Sir Isaac Newton observed that planets exhibited retrograde motion across the night sky.

A - Because Sir Francis Galton observed that, when fathers were above average in height, so were their sons, though not as much

A parameter is a number that describes some aspect of Select one: a. a proportion. b. a sample. c. a statistic. d. a population.

A - a population

What is it that causes the sample mean 𝑥⎯⎯⎯x¯ to be an unbiased estimator for the population mean 𝜇μ? Select one: a. Doing simple random sampling. b. Increasing the sample size n. c. Doing theoretical calculations. d. Using simulation.

A - doing simple random sampling

What is the key to making the math we do simpler than it would be otherwise? Select one: a. doing simple random sampling. b. using many summation formulas. c. making the variance smaller. d. using large sample sizes n.

A - doing simple random sampling

Which of the following things is the most essential in helping you understand and do problems related to Normal curves? Select one: a. Drawing an accurate representation of the Normal curve, as well as points on the axis and related areas. b. Using your calculator. c. Using Table D d. Saying that z = P.

A - drawing an accurate representation of the Normal curve, as well as points on the axis and related areas

For a continuous variable X whose values are determined by a density curve, how should you find probabilities that X is in a certain range of values by Select one: a. finding the area under the density curve above that range of values. b. finding how high the density curve goes. c. finding how steep the density curve is. d. finding the average value of the density curve.

A - finding the area under the density curve about that range of values

The mean of a density curve is best described as Select one: a. the balance point to put the fulcrum at if the density curve were a mass sitting on a see-saw. b. the distance between the peak and the inflection points on either side of the peak. c. the point of equal areas, where half the area is to the left and half the area is to the right. d. the location of the peak (highest point) of the curve.

A - the balance point to put the fulcrum at if the density curve were a mass sitting on a see-saw

The sampling distribution of a statistics is Select one: a. the distribution of values taken by the statistic in all possible samples of the same size from the population.the distribution of values taken by the statistic in all possible samples of the same size from the population. b. the extent to which the sample results differ systematically from the truth. c. the mechanism that determines whether randomization was effective. d. the probability that we obtain the statistic in repeated random samples.

A - the distribution of values taken by the statistic in all possible samples of the same size from the population.the distribution of values taken by the statistic in all possible samples of the same size from the population.

The five-number summary consists of Select one: a. the minimum, first quartile, median, third quartile, and maximum. b. the mean, median, standard deviation, range, and interquartile range. c. the mean, standard deviation, skewness, kurtosis, and median. d. the range, maximum, minimum, fifth quartile, and interquartile range.

A - the minimum, first quartile, median, third quartile, and maximum

When a coin is said to be "fair", that means Select one: a. the probability of heads (or tails) is assumed to be 0.5 = 50%. b. the probability of heads (or tails) is most definitely, without a doubt, exactly 0.5 = 50%. c. somebody bought the coin from a fair-trade country. d. it's a nice-looking coin.

A - the probability of heads (or tails) is assumed to be 0.5 = 50%

The fraction of the variation in y that is explained by the least squares linear regression line of y on x is equal to Select one: a. the squared correlation r^2 b. the correlation r c. the intercept b0 d. the slope b1

A - the squared correlation r^2

By definition, SSxx equals Select one: a. =∑(x−x(bar))^2 b. =∑x(bar)^2 c. =∑x^2 d. =∑(𝑥𝑥)^2

A - ∑(x−x(bar))^2

In essence, the Central Limit Theorem says that, when drawing a simple random sample from a population with mean 𝜇μ and standard deviation 𝜎σ, the sampling distribution of the sample mean 𝑥⎯⎯⎯x¯ is approximately Select one: a. Binomial with mean 𝜇μ and standard deviation 𝜎σ. b. Normal with mean 𝜇μ and standard deviation 𝜎𝑛√σn. c. Normal with mean 𝜇μ and standard deviation 𝜎σ. d. Binomial with mean 𝜇μ and standard deviation 𝜎𝑛√σn.

B

Use Table A (or your calculator) to find the area under the standard Normal curve N(0,1) to the left of z = 1.54. Select one: a. .0618 b. .9382 c. .0630 d. .9370

B - .9382

Suppose a population of students has a mean SAT score of 𝜇=550μ=550 and standard deviation of 𝜎=100σ=100. For a simple random sample of size 𝑛=25n=25, find the probability that the sample mean score is greater than or equal to 580. In probability notation, find 𝑃(𝑥⎯⎯⎯≥580 | 𝜇=550)P(x¯≥580 | μ=550). (Note: you will need a table and/or a calculator to do this problem). Select one: a. 0.1600 b. 0.0668 c. 0.0250 d. 0.0486

B - 0.0668

Suppose A and B are independent events with 𝑃(𝐴)=0.4P(A)=0.4 and 𝑃(𝐵)=0.3P(B)=0.3, then the value of 𝑃(𝐴 and 𝐵)P(A and B) is a. 0.75 b. 0.12 c. 0.10 d. 0.70

B - 0.12

If 𝜇=5, 𝜎=2, and 𝑥=4, then the z-score is 𝑧= Select one: a. -1 b. -0.5 c. 0.5 d. 1

B - 0.5

If A and B are disjoint events with 𝑃(𝐴)=0.4P(A)=0.4 and 𝑃(𝐵)=0.3P(B)=0.3, then the value of 𝑃(𝐴 or 𝐵)P(A or B) is a. 0.75 b. 0.70 c. 0.12 d. 0.10

B - 0.70

What are the two main ways of demonstrating facts about sampling distributions? (For example, the fact that, when doing simple random sampling, the sampling distribution of the sample mean is centered on 𝜇μ and has standard deviation 𝜎𝑛√σn ). Select one: a. 1) abstract mathematical reasoning ("proofs") and 2) scientific reasoning b. 1) abstract mathematical reasoning ("proofs") and 2) simulation. c. 1) playing games of chance and 2) scientific reasoning d. 1) simulation and 2) playing games of chance

B - 1) abstract mathematical reasoning ("proofs") and 2) simulation

The formula for the standard deviation 𝜎𝑋σX of a discrete random variable X with finitely many values is, in sloppy notation, 𝜎𝑋=∑(𝑥−𝜇𝑋)2⋅𝑝‾‾‾‾‾‾‾‾‾‾‾‾‾‾√σX=∑(x−μX)2⋅p. To use this formula, you should do which steps? (in the order they appear) Select one: a. 1) add, 2) take a square root, 3) find the differences, 4) find the mean of X, 5) square the differences, 6) find the products of the differences times the corresponding probabilities. b. 1) find the mean of X, 2) find the differences, 3) square the differences, 4) find the products of the differences times the corresponding probabilities, 5) add those products, 6) take a square root. c. 1) take a square root, 2) add, 3) find the mean of X, 4) find the differences, 5) square the differences, 6) find the products of the differences times the corresponding probabilities. d. 1) square the differences, 2) find the products of the differences times the corresponding probabilities, 3) add, 4) find the differences, 5, take a square root, 6) find the mean of X.

B - 1) find the mean of X, 2) find the differences, 3) square the differences, 4) find the products of the differences times the corresponding probabilities, 5) add those products, 6) take a square root.

For a probability model with finitely many outcomes, the key properties that make the model legitimate are: Select one: a. 1) no probability is above one and 2) the probabilities match what happens in reality. b. 1) for each possible outcome, the probability is not negative (it's greater than or equal to zero) and 2) all the probabilities add to one. c. for each possible outcome, the probability is not negative (it's greater than or equal to zero) and 2) the probabilities match what happens in reality. d. 1) the probabilities add to one and 2) the probabilities match what happens in reality.

B - 1) for each possible outcome, the probability is not negative (it's greater than or equal to zero) and 2) all the probabilities add to one.

If a regression line has equation 𝑦ˆ=4+3𝑥y^=4+3x and 𝑥=5x=5, then the predicted value of 𝑦y is Select one: a. 35 b. 19 c. 4 d. 4

B - 19

A statistics exam has a mean score of 82 points and a standard deviation of 8 points. To the nearest whole number, find the exam score at the 60th percentile. Select one: a. 86 b. 84 c. 60 d. 88

B - 84

Which of the following is one of the most important properties of simple random sampling (assuming we have a large enough sample size)? Select one: a. It produces samples that are typically the entire population. b. It produces samples that are representative of the population. c. It produces samples that are biased. d. It produces samples that are bigger than needed.

B - It produces samples that are representative of the population

In Statistics, SS almost always stands for Select one: a. Sum of Slopes b. Sum of Squares c. Sum of Slytherins d. Sum of Sieves

B - Sum of Squares

For Normally distributed data, about what percent will lie within 2 standard deviations of the mean? Select one: a. about 20%. b. about 95%. c. about 99.7%. d. about 68%.

B - about 95%

The main application of probability theory for our class will be for Select one: a. using statistical formulas. b. doing statistical inference. c. calculating correlations. d. doing descriptive statistics.

B - doing statistical inference

For a continuous variable X whose values are determined by a density curve, how should you find probabilities that X is in a certain range of values by Select one: a. finding how steep the density curve is. b. finding the area under the density curve above that range of values. c. finding the average value of the density curve. d. finding how high the density curve goes.

B - finding the area under the density curve above that range of values

What is the meaning of the expression (∑𝑥)2(∑x)2? Select one: a. The order doesn't matter. You can either square the x-values and then add those squares, or you can add the x-values and then square that sum. b. First, add the x-values, then square that sum. c. 42, the answer to life, the universe, and everything (Google it!)...haha...but this is the wrong answer to this question...pick something else (seriously) d. First, square the x-values, then add those squares.

B - first, add the x-values, then square that sum

What is the name of a kind of variable that can be a common cause for two associated variables? For example, the amount of smoking a person does and their likelihood of getting cancer show a positive association. Is it possible that genetics is a common cause of both cancer and the likelihood of smoking? If so, then what do we call this kind of variable? Select one: a. Independent variable b. Lurking variable c. Sustaining variable d. Dependent variable

B - lurking variable

A sample mean 𝑥(bar) is unbiased if Select one: a. voluntary response sampling is done. Because having volunteers is always better than forcing people to do a survey, which would cause them to be mad an introduce bias. b. simple random sampling is done, so that the mean of the sampling distribution of 𝑥(bar) is equal to the population mean 𝜇, written as 𝜇𝑥(bar)=𝜇. This means 𝑥(bar) does not tend to systematically overestimate or underestimate 𝜇 in repeated random sampling. c. the researcher has no biases beforehand. The researcher doesn't know what to expect and has no hypotheses about what he or she thinks will happen. This helps the researcher do a correct calculation of 𝑥(bar) so that it is not biased with the wrong answer. d. simple random sampling is done, so that the standard deviation of the sampling distribution of 𝑥(bar) is equal to 𝜎𝑛√σn, written 𝜎𝑥(bar)=𝜎𝑛√σx¯=σn. This means that the variability in the values of 𝑥(bar) decreases as 𝑛n increases.

B - simple random sampling is done, so that the mean of the sampling distribution of 𝑥(bar) is equal to the population mean 𝜇, written as 𝜇𝑥(bar)=𝜇. This means 𝑥(bar) does not tend to systematically overestimate or underestimate 𝜇 in repeated random sampling.

For a discrete random variable X which can take on finitely many values with corresponding probabilities, the formula for the mean 𝜇𝑋μX of X is Select one: a. 𝜇𝑋=∑𝑥μX=∑x. b. 𝜇𝑋=∑𝑥⋅𝑝μX=∑x⋅p. c. 𝜇𝑋=∑𝑝μX=∑p. d. 𝜇𝑋=∑(𝑥+𝑝)μX=∑(x+p).

B - 𝜇𝑋=∑𝑥⋅𝑝μX=∑x⋅p.

The standard deviation of X + Y, denoted 𝜎𝑋+𝑌σX+Y, is related to the standard deviations of X and Y individually, 𝜎𝑋σX and 𝜎𝑌σY, by the equation Select one: a. 𝜎𝑋+𝑌=𝜎2𝑋+𝜎2𝑌‾‾‾‾‾‾‾‾√σX+Y=σX2+σY2, no matter what the relationship between X and Y is. b. 𝜎𝑋+𝑌=𝜎𝑋+𝜎𝑌σX+Y=σX+σY, but only if X and Y are independent. c. 𝜎𝑋+𝑌=𝜎2𝑋+𝜎2𝑌‾‾‾‾‾‾‾‾√σX+Y=σX2+σY2, but only if X and Y are independent. d. 𝜎𝑋+𝑌=𝜎𝑋+𝜎𝑌σX+Y=σX+σY, no matter what the relationship between X and Y is.

C

Which spreadsheet function will give you areas under a Normal curve? Select one: a. =NORM b. =NORMINV c. =NORMDIST d. =NORMAL

C - =NORMDIST

Identify the problem with the following statement: "The correlation between planting rate, in beans per second, and yield of soybeans, in bushels per acre, was found to be r = 0.23 bushel. Select one: a. The correlation cannot be found because yield of corn is a categorical variable. b. The correlation cannot be found because planting rate is a categorical variable. c. Correlations don't have units. d. The correlation is a c value, not an r value.

C - Correlations don't have units

A statistics exam has a mean score of 82 points and a standard deviation of 8 points. To the nearest whole number, find the exam score at the 60th percentile. Select one: a. 60 b. 86 c. 88 d. 84

D - 84

Which of the following statements is false about density curves? Select one: a. The mean of any density curve is the balance point at which it would balance if it were made of solid material. b. Density curves have a total area under them equal to 1. c. Density curves are always on or above the horizontal axis. d. Density curves must be symmetric. No skewness is allowed

D - Density curves must be symmetric. No skewness is allowed

Which spreadsheet function will give you areas under a Normal curve? Select one: a. =NORMINV b. =NORM c. =NORMAL d. =NORMDIST

D - NORMDIST

For an event labeled with the letter A, which of the following expressions represents the fact that the probability of A occurring is 0.2? Select one: a. 𝐴=0.2 b. 𝑃=0.2 c. 𝑃(0.2) d.𝑃(𝐴)=0.2

D - P (A) = 0.2

Which is the symbol for the quantity that the least squares linear regression line minimizes? Select one: a. SSR b. SSyy c. SSS d. SSE

D - SSE

Which of the following are a list or properties of well-designed experiments to test, for example, the effectiveness of a new drug? In other words, which of the following properties gives the best chance of proving that a new drug works or concluding that it is no better than a placebo. Select one: a. The experiment should be bound by the factors, determined by the treatments, and responded to. b. The experiment should be overseen by people who care about the patients, can empathize with them, and encourage them. c. The experiment should be done with proper equipment, overseen by the CEO, and well funded. d. The experiment should be randomized, controlled, double blind, and large sample.

D - The experiment should be randomized, controlled, double blind, and large sample

In the videos, what was the first example used to illustrate the idea of a sampling distribution? Select one: a. The heights of flowers in a garden and the mean heights of random samples of these flowers. b. The weights of dogs in a dog show and the mean weights of random samples of these dogs. c. The weights of bags of candy coming out of a factory and the mean weights of random samples of these bags of candy. d. The heights of children on a playground and the mean heights of random samples of these children.

D - The heights of children on a playground and the mean heights of random samples of these children

Identify the problem with the following statement: "The correlation between planting rate, in beans per second, and yield of soybeans, in bushels per acre, was found to be r = 0.23 bushel. Select one: a. The correlation cannot be found because yield of corn is a categorical variable. b. The correlation is a c value, not an r value. c. The correlation cannot be found because planting rate is a categorical variable. d. Correlations don't have units.

D - correlations don't have units

What is it that causes the sample mean 𝑥(bar) to be an unbiased estimator for the population mean 𝜇μ? Select one: a. Doing theoretical calculations. b. Increasing the sample size n. c. Using simulation. d. Doing simple random sampling. Feedback

D - doing simple random feedback

The sampling distribution of a statistics is Select one: a. the extent to which the sample results differ systematically from the truth. b. the mechanism that determines whether randomization was effective. c. the probability that we obtain the statistic in repeated random samples. d. the distribution of values taken by the statistic in all possible samples of the same size from the population.the distribution of values taken by the statistic in all possible samples of the same size from the population.

D - the distribution of values taken by the statistic in all possible samples of the same size from the population.the distribution of values taken by the statistic in all possible samples of the same size from the population

The fraction of the variation in y that is explained by the least squares linear regression line of y on x is equal to Select one: a. the slope b1 b. the correlation r c. the intercept b0 d. the squared correlation r^2

D - the squared correlation r^2

The main purpose of a stemplot is Select one: a. to help us compute the mean of the data. b. to help us ultimately make a scatterplot of the data. c. to break the data into stems and leaves for the purpose of seeing why the data are useful. d. to see the distribution, or "shape", of the data.

D - to see the distribution, or "shape", or the data

When you look at a stemplot to see the shape of the data, you should Select one: a. tip your head to be at a 45 degree angle backward. b. tip your head to be at a 45 degree angle forward. c. turn your head sideways so that the top of your head is pointing to the left. d. turn your head sideways so that the top of your head is pointing to the right.

D - turn your head sideways so that the top of your head is pointing to the right

Which of the following is the spreadsheet function that returns an x-value for a given area for a Normal curve? Select one: a. =NORM b. =NORMAL c. =NORMDIST d. =NORMINV

D- NORMINV

Convenience sampling is a good sampling method because it is easy to do. Select one: True False

False

Historically, it was very easy to prove that smoking causes lung cancer. It was a very logical conclusion based on the fact that people who smoked got cancer more often, plus the fact that cigarette smoke is so unpleasant. Select one: True False

False

If two quantitative variables x and y have a very strong nonlinear relationship, then the correlation r will typically be very close to 1. Select one: True False

False

In picking one card at random from a well-shuffled standard deck of 52 cards, the events that "the card is a Diamond" and "the card is Red" are independent. Select one: True False

False

Since a census attempts to count everyone in a population, it is always the best method for obtaining statistical information. Select one: True False

False

The Law of Large Numbers says that, when doing simple random sampling (getting independent observations) from a population with finite mean 𝜇μ, the sample mean 𝑥⎯⎯⎯x¯ gets closer and closer to 𝜇μ as the number of observations n increases, without ever having any ups and downs. Select one: True False

False - The sample mean 𝑥(bar) does get closer and closer to 𝜇μ as the number of observations n increases, but there can definitely be some ups and downs.

√=3^2+4^2=3+4 Select one: True False

false

On a TI calculator, you should use "s" for the sample standard deviation. You should NOT use the Greek letter sigma σ. Select one: True False

true

The quantity 𝑧=(𝑥−𝜇)/𝜎z=(x−μ)/σ tells us how many standard deviations x is above or below the mean 𝜇μ. Select one: True False

true