Stats Exam 2 Practice Test

T/F The shape of the histogram of sample data gets closer to the shape of the population as the sample size increases

True

Which one of the following is NOT affected by outliers? A. mean B. median C. standard deviation D. correlation coefficient E. slope

B

T/F x-bar gets closer and closer to mew as n increases

True

T/F 95% of all possible x-bar's will be within 2 sigma of mew

False

Symbol: Mean of a population

Mew

Symbol: Mean of a sample

x-bar

Symbol: Z-score formula for standardizing an observed sample mean

z= (x-bar - mew)/(sigma/square root(n))

Symbol: The standard deviation of the sampling distribution of x-bar

Sigma/Square root(n)

Symbol: Z-score formula for standardizing an observation on an individual.

z= (x - mew)/sigma

Fill in the blank: Central Limit Theorem allows us to compute probabilities on ___________ using the standard Normal table provided the sample size of the random sample is sufficiently large. A. x-bar B. μ C. s D. sample measurements.

A

The value of a parameter will only change if A. the population changes. B. a different sample is obtained from the population. C. the sample size is increased. D. repeated samples are taken from the same population.

A

(See 19 on practice test) The probability distribution for the number of cars owned by family units is listed as follows: # of cars = x 0 1 2 3 4 5 P(x) .07 .21 .44 .22 .05 .01 What is the probability that a randomly selected family unit owns at least two cars? A. .000484 B. .0968 C. .44 D. .72 E. .93

D

The Central Limit Theorem tells us that under certain conditions A. the shape of the histogram of the sample data will have the same shape as the population from which the sample was taken. B. the mean and standard deviation of the sample will be approximately equal to the mean and standard deviation of the population from which we sample. C. the shape of the population from which we sample will be approximately Normal. D. the shape of the data in the sample will be approximately Normal. E. the shape of the sampling distribution of x-bar will be approximately Normal.

E

The mean score of the fourth exam in a statistics class with 1800 students at a large university was 79 with a standard deviation of 14. Suppose twenty-five students are to be randomly selected and their sample mean computed. What will be the mean and standard deviation of the sampling distribution of x-bar? A. 3.16, 0.56 B. 15.8, 0.56 C. 15.8, 2.8 D. 79.0, 14 E. 79.0, 2.8

E

T/F The mean of the theoretical sampling distribution of x-bar gets closer to mew as n increases.

False

Symbol: Mean of the sampling distribution of x-bar

Mew

(See 44 on practice test) Eight hundred students at a local junior college were asked if they favored a ban on cell phone usage in the school cafeteria. The results of the survey are as follows: Favor Oppose No Opinion Total Males 153 176 71 400 Females 235 111 54 400 Total 388 287 125 800 What proportion of the students surveyed opposes a ban on cell phone usage in the school cafeteria? A. 0.359 B. 0.383 C. 0.394 D. 0.485 E. 0.613

A

(See 44) Refer to the above table. What is the conditional distribution of opinion for males? A. 38.3%, 44.0%, 17.8% B. 39.4%, 61.3%, 56.8% C. 58.8%, 27.8%, 13.5% D. 60.6%, 38.7%, 43.2%

A

(See 57 on Practice test) Fill in the blank: The correlation coefficient computed on the data set in this scatterplot that includes both outliers is ___________________ the correlation coefficient computed on the data set with the two outliers deleted. A. closer to zero than B. the same as C. farther from zero than

A

Control charts are designed to sound an alarm when A. the amount of observed variation exceeds the amount that could be attributable to natural variation. B. variation is observed in the x-bar's. C. the observed sample means differ from the control standard by an amount attributable to natural variation. D. the sample mean, x-bar, differs from the control standard by even a small amount.

A

Correlation coefficient, r, should only be calculated when A. two variables, x and y, are quantitative and their relationship is linear. B. there is clearly an association between x and y. C. the points in the scatterplot can be connected to form a line. D. x and y are bivariate categorical.

A

Extrapolation is dangerous because A. the relationship between X and Y may be different outside the range of observed x's. B. the increase in the variability of the y's across all x's may affect the prediction. C. the least squares regression equation may be influenced by outliers (i.e., influential points). D. we can't say changes in X cause changes in Y even when a relationship exists between X and Y.

A

Fill in the blank: For the sampling distribution of x-bar created by taking random samples from a left skewed population, the standard deviation of x-bar ____________ as n increases. A. decreases B. stays the same C. increases

A

Lifetimes of a particular flashlight battery have a non-Normal distribution with mean, mew, of 35.6 hours and standard deviation sigma = 5.4 hours. A quality inspector is planning to take a random sample of 43 of these batteries and compute the sample mean. Can he compute the probability that the sample mean will exceed 35.7 hours using the standard Normal table? Why or why not? A. Yes, because the sample will be large and random so the Central Limit Theorem applies. B. Yes, because the original population was normally distributed and sample will be random. C. No, because the sample size is too small to apply the Central Limit Theorem. D. No, because the original distribution was not normally distributed.

A

The X variable in regression is called A. the explanatory variable. B. the horizontal variable. C. the response variable. D. the lurking variable. E. the extraneous variable.

A

The least squares regression line is the line for which A. the sum of the squared residuals is minimized. B. the sum of the vertical distances of the points to the line is minimized. C. the squared deviations of the points about their mean is as small as possible. D. the prediction errors about the line are made as small as possible.

A

The standard deviation of a sampling distribution for x-bar is _____________ the standard deviation of the population from which samples of size n >1 are taken to create the sampling distribution. A. less than B. equal to C. greater than D. not comparable with

A

The vertical distance from a point to the regression line is called A. residual. B. correlation coefficient. C. standard deviation. D. round off error. E. yˆ (y-hat).

A

Twenty-five right-handed men were tested to compare their right hand strength with their left hand strength using a bathroom scale. For each male, a coin was tossed. If it landed heads, the man first squeezed the scales with his right hand and then with his left hand. If the coin landed tails, the man squeezed the scales with his left hand first and then with his right. The weight registered on the scale is recorded for both hands. What type of study is this? A. Matched pairs experiment B. Completely random experiment C. Observational study D. Simple random sample

A

Which one of the following does NOT have variability? A. a parameter B. data C. a statistic D. a random variable E. a quantitative response variable

A

Which one of the following is not a statistic? A. μ B. x-bar C. ˆp (p-hat) D. s E. median of data in a sample

A

A theoretical sampling distribution of a statistic consists of A. the results of a sample. B. the values of a statistic from all possible samples. C. the range of the values in a sample. D. a set of sample data that has the shape as the original population.

B

Do you need to apply the Central Limit Theorem to compute the probability on the mean weight of 16 randomly selected bags described in the above question? A. No, because the individual was not randomly selected. B. No, because the distribution of weights is Normally distributed. C. Yes, because we used the standard Normal table. D. Yes, because the sample was random and n was large.

B

Fill in the blank: For the sampling distribution of x-bar created by taking random samples from a left skewed population, the shape is _______________ for large n. A. skewed right B. approximately Normal C. skewed left

B

The Central Limit Theorem on x-bar requires A. the sample size is less than 10% of the population. B. a large random sample. C. z= (x-bar-mew)/(sigma/square root(n)) D. Normality of the sampled population.

B

The Central Limit Theorem says that A. the sample mean x-bar gets closer and closer to μ as sample size increases. B. the sampling distribution of x-bar is approximately Normal when the samples are large and random. C. the population from which we sample can be transformed to a Normal distribution using standard scores (z-scores). D. the shape of the histogram of observations in a sample gets more and more Normal as sample size increases.

B

The probability of an event can be defined as A. 1 / k where k is the number of possible outcomes of which the event is one possible outcome. B. the fraction of time the event will occur if the random phenomenon is repeated many times. C. the average number of times that the event will occur in the long run. D. the odds of the event occurring; i.e., k to 1.

B

To detect association between the row and column variables of a two-way table, what do we examine? A. Whether the proportions in the marginal distribution of the column variable are decreasing, increasing, or staying constant. B. Whether the conditional distribution in every row (or every column) equals the corresponding marginal distribution. C. Whether the value in each cell divided by the table total equals the value in the row total divided by the table total. D. Whether a lurking variable interacts with both the row and column variables.

B

Twelve members of a college women's golf team played two rounds of golf in a tournament. The correlation between their scores on the first round with their respective scores on the second round was .687. What percentage of the variation in their scores on the second round can be explained by their scores on the first round? A. 31.3% B. 47.2% C. 68.7% D. 82.9%

B

What is the purpose of a scatterplot? A. to determine whether the data are normally distributed. B. to visually assess the relationship between X and Y. C. to specify the distribution of the data. D. to identify the amount of kurtosis in the data.

B

Data collected on 16 males was used to model the relationship between neurons per gram of tissue, y, and age in years, x. Use the regression equation yˆ (y-hat) = 5.21 + .035x. Male who is 70 years old. (Note: r = .761) On the basis of the study described in the above two questions, what percentage of the variation in neurons per gram of tissue can be explained by age in years? A. 76.1% B. 57.9% C. 33.5% D. 5.21%

B (r^2)

A manufacturing process produces bags of cookies that have Normally distributed weights with a mean of μ = 15.0 oz. and a standard deviation of sigma = 0.4 oz Referring to the manufacturing process in question 15 above, what are the lower and upper limits for the control chart for x-bar from samples of size 16? A. 13.8, 16.2 B. 14.6, 15.4 C. 14.7, 15.3 D. 14.9, 15.1

C

A random sample of size 10 was taken from a population. The sample has a standard deviation of zero. Which of the following statements must be true. A. The population has a standard deviation of zero. B. The sample mean is greater than the sample median. C. The ten data points in the sample are all equal in numerical value. D. The sample size is too small to compute standard deviation.

C

For the theoretical sampling distribution of x-bar created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and sigma = 4 For the sampling distribution of x-bar described in question 11, what is its shape? A. Slightly right skewed B. Approximately Normal C. Slightly left skewed D. Cannot be determined without knowing the shape of the population.

C

For the theoretical sampling distribution of x-bar created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and sigma = 4 Referring to the sampling distribution of x-bar described in question 11, what is the standard deviation of the sampling distribution of x-bar? A. 5.5 B. 4.0 C. 1.0 D. 0.25 E. 0.0625 F. Cannot be determined

C

For the theoretical sampling distribution of x-bar created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and sigma = 4, the mean of this sampling distribution A. is approximately equal to 22. B. is slightly less than 22. C. is exactly equal to 22. D. is slightly greater than 22. E. would approach 22 if the sample size were to continually increase.

C

Lifetimes of a particular flashlight battery have a non-Normal distribution with mean, mew, of 35.6 hours and standard deviation sigma = 5.4 hours. A quality inspector is planning to take a random sample of 43 of these batteries and compute the sample mean. Referring to the above question and assuming that computing the probability is okay, what is the probability that the sample mean exceeds 35.7? A. 0. 8786 B. 0.5478 C. 0.4522 D. 0.1214 E. 0.0185

C

The announcer on the radio tells listeners that the probability of snow tonight is 20%. We should interpret this to mean that A. 20% of the listeners will have snow in their area tonight. B. you will not have any snow tonight because the chance of snow is less than 50%. C. according to historical records when meteorological conditions were the same as today, it snowed twenty percent of the time. D. it will snow if you are unlucky (or lucky if you like snow) and not snow if you are lucky.

C

Twelve members of a college women's golf team played two rounds of golf in a tournament. The correlation between their scores on the first round with their respective scores on the second round was .687 (Refer to the previous question.) Using the scores on the first round to predict the scores on the second round, we obtain the least squares regression equation as: round2 = 26.3 + 0.688 round1. For each one point increase in the scores on the first round, on the average how much can a player expect her scores to increase on the second round? A. .311 B. .687 C. .688 D. 26.3

C

Two variables, x and y, are said to have a positive relationship if A. the points lie very close to a line. B. the absolute values of y are approximately the same size as the absolute values of x. C. the y values increase as the x values increase. D. most of the total variation in y can be explained by the x variable.

C

What is a distribution of a random variable? A. The range of the values of a variable as centered around the mean. B. The numerical values placed on a histogram at varying points about the mean. C. A list of the possible values of a variable together with how often each value occurs. D. The position of a variable within an observed data set.

C

A correlation of r = 0 indicates that A. no relationship of any form exists between x and y. B. x does not cause changes in y. C. the total variation in x cannot be explained by y. D. x and y are not linearly related.

D

Data collected on 16 males was used to model the relationship between neurons per gram of tissue, y, and age in years, x. Use the regression equation yˆ (y-hat) = 5.21 + .035x. Male who is 70 years old. (Note: r = .761) On the basis of the study described in the above question, as a male gets one year older, by how much can he expect his neurons per gram of tissue to increase per year on the average? A. 5.21 B. 0.761 C. 0 .579 D. 0.035

D

Data collected on 16 males was used to model the relationship between neurons per gram of tissue, y, and age in years, x. Using the regression equation yˆ (y-hat) = 5.21 + .035x that was obtained from the data, find the predicted neurons per gram of tissue for a male who is 70 years old. (Note: r = .761) A. 362.25 B. 6 C. 2.76 D. 7.66

D

On a control chart, under what circumstance is the process out of control? A. A run of 9 sample means above the centerline or below the centerline B. A sample mean below the lower limit C. A sample mean above the upper limit D. All of the above E. None of the above

D

What is the random variable of the sampling distribution of x-bar? A. the parameter being estimated B. the response variable C. the observations in the sample D. the sample mean

D

(See #56 on Practice test) This scatterplot displays bivariate data where x = diameter of a tree and y = volume of wood produced by the tree. What is the correlation for these data? A. -0.88 B. -0.41 C. 0.06 D. 0.53 E. 0.87

E

A manufacturing process produces bags of cookies that have Normally distributed weights with a mean of μ = 15.0 oz. and a standard deviation of sigma = 0.4 oz. What is the probability that a randomly selected bag weighs more than 15.2 oz? A. 0.9772 B. 0.6915 C. 0.5793 D. 0.5000 E. 0.3085 F. 0.0228

E

A manufacturing process produces bags of cookies that have Normally distributed weights with a mean of μ = 15.0 oz. and a standard deviation of sigma = 0.4 oz Referring to the manufacturing process described in the above question, what is the probability that 16 randomly selected bags have a mean weight that exceeds 15.2 oz? A. 0.9772 B. 0.6915 C. 0.5793 D. 0.5000 E. 0.3085 F. 0.0228

F

T/F Central Limit Theorem allows us to compute probabilities on sample data from a non-Normal population whenever the sample size is large and random.

False

T/F If all of the row conditional distributions equal the marginal distribution for the bottom row, then the row variable is associated with the column variable.

False

T/F Scatterplots can be used to assess the strength of association for the variables of a two-way table

False

T/F The shape of the theoretical sampling distribution of x-bar is always Normal.

False

T/F The value of a sample statistic usually equals the value of the parameter of the population from which the sample was taken.

False

T/F Data in a scatterplot can be made to look more scattered (or concentrated) about a regression line by stretching (or shrinking) the scale of the y axis

True

T/F Probabilities on individuals can only be computed using the standard Normal table if the population is Normally distributed

True

T/F Standard deviation of x-bar is a shorter way of saying standard deviation of the sampling distribution of x-bar .

True

T/F Standard deviation of x-bar is computed using sigma/square root(n)

True

(See 44) Refer to the above table. What proportion of the males favor a ban on cell phone usage in the school cafeteria? A. 0.359 B. 0.383 C. 0.394 D. 0.485 E. 0.613

B

The standard deviation of the sampling distribution of x-bar measures A. the variability of observations about the mean. B. the variability of the sample mean values about the parameter, μ. C. the height of the sampling distribution. D. the error or difference between the value of a statistic and its parameter.

B

Which one of the following measures the variability of a statistic? A. the standard deviation of the data. B. the standard deviation of the sampling distribution for the statistic. C. the total sum of squares of deviations of the observations about the mean. D. the number of standard deviations that a statistic value differs from the parameter value.

B

Correlation coefficient is a measure of A. concentration of data about the mean. B. how far the data are on average from the straight line regression equation. C. the strength of the linear relationship between x and y. D. how many standard deviations an observation is from the mean.

C

The sampling distribution of a statistic has all of the following except A. shape. B. center. C. spread. D. correlation.

D

Which one of the following does NOT have the same units of measure as the data? A. mean B. median C. standard deviation D. correlation coefficient E. residual

D

Which one of the following is NOT a parameter? A. the mean of the measurements on all the individuals in a population. B. the proportion of a population that have a certain characteristic. C. the standard deviation of an entire population. D. the proportion in a survey that favor a certain opinion.

D

Symbol: Standard deviation of a population

Sigma

T/F The standard deviation of x-bar (for n > 1) is always less than the standard deviation of the population

True

Symbol: Standard deviation of data in a sample.

s

When you play solitaire, you either win or lose. Therefore, the probability of winning, according to its definition, is A. .5 because you either win or lose. B. approximated by playing lots of times and dividing the number of times you win by the number of times you play. C. impossible to compute. D. computed from the number of possible ways the deck of cards can be dealt.

B

T/F A correlation coefficient, r, close to +1.0 implies changes in x cause changes in y

False

T/F A correlation of zero means no relationship exists between x and y

False

T/F 95% of all possible x-bar's will be within 2 sigma/square root(n) of mew

True

T/F A statistic varies because each random sample yields a different value for the statistic

True