The bookstore of a large university wants to determine how much money full-time first-year students spend, on average, in the university bookstore. At the end of the school year, a random sample of bookstore bills for 40 first-year students is obtained. A 95% confidence interval for the mean is calculated to be ($450, $1300). Which of the following is a correct interpretation of this interval?

The bookstore of a large university wants to determine how much money full-time first-year students spend, on average, in the university bookstore. At the end of the school year, a random sample of bookstore bills for 40 first-year students is obtained. A 95% confidence interval for the mean is calculated to be ($450, $1300). Which of the following is a correct interpretation of this interval?

A) We can be 95% confidence that the average bookstore bill for full-time first-year students in our sample is between $450 and $1300.
B) We can be 95% confident that the average bookstore bill for full-time first year university students is between $450 and $1300
C) We can be 95% confident that the average bookstore bill for full-time first-year students at this university is between $450 and $1300
D) The average bookstore bill for full-time first-year students at this university will be between $450 and $1300 about 95% of the time
E) About 95 out of 100 full-time first-year students at this university will have bookstore bills between $450 and $1300

Two agronomists analyzed the dame data, testing the same null hypothesis about the proportion of tomato plants suffering from blight. One rejected the hypothesis but the other did not. Assuming neither made a mistake in calculations, which of these possible explanations could account for this apparent discrepancy?

Two agronomists analyzed the dame data, testing the same null hypothesis about the proportion of tomato plants suffering from blight. One rejected the hypothesis but the other did not. Assuming neither made a mistake in calculations, which of these possible explanations could account for this apparent discrepancy?

I. One agronomist wrote a one-tailed alternative hypothesis
II. They wrote identical hypotheses, but the one who rejected the null used a higher x- level.
III. They wrote identical hypotheses, but the one who rejected the null used a lower x-level.


A) I and II
B) I only
C) III only
D) I and III
E) II only

Answer: A

The federal guideline for smog is 12% pollutants per 10,000 volume of air. A metropolitan city is trying to bring its smog level into federal guidelines. The city comes up with a new policy where city employees are to use city transportation to and from work. A local governmental group does not think the city is doing enough and no real decrease will occur. An independent agency, hired by the city, runs its test and comes up with a P-value of 0.055. What is reasonable to conclude about the new strategy using a x=0.025?

The federal guideline for smog is 12% pollutants per 10,000 volume of air. A metropolitan city is trying to bring its smog level into federal guidelines. The city comes up with a new policy where city employees are to use city transportation to and from work. A local governmental group does not think the city is doing enough and no real decrease will occur. An independent agency, hired by the city, runs its test and comes up with a P-value of 0.055. What is reasonable to conclude about the new strategy using a x=0.025?

A) There is a 94.5% chance of the new policy having no effect on smog.
B) There is a 5.5% chance of the new policy having no effect on smog.
C) There's only a 5.5% chance of seeing the new policy having no effect on smog in the results we observed from natural sampling variation. We conclude the new policy is more effective.
D) We can say there is a 5.5% chance of seeing the new policy having no effect on smog in the results we observed from natural sampling variation. There is no evidence the new policy is more effective, but we cannot conclude the policy has no effect on smog.
E) We can say there is a 5.5% chance of seeing the new policy having an effect on smog in the results we observed from natural sampling variation. We conclude the new policy is more effective.

Answer: D

At one SAT test site students taking the test for the second time volunteered to inhale supplemental oxygen 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help test-takers think more clearly?

At one SAT test site students taking the test for the second time volunteered to inhale supplemental oxygen 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help test-takers think more clearly?

A) 1-sample t-test
B) 2-proportion z-test
C) matched pairs t-test
D) 2-sample t-test
E) 1- proportion z-test

Answer: B

At one vehicle inspection station, 13 of 52 trucks and 11 of 188 cars failed the emissions test. Assuming these vehicles were representative of the cars and the trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?

At one vehicle inspection station, 13 of 52 trucks and 11 of 188 cars failed the emissions test. Assuming these vehicles were representative of the cars and the trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?

A) 0.032
B) 0.095
C) 0.070
D) 0.025
E) 0.049

Answer: C

Absorption rates into the body are important considerations when manufacturing a generic version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test H0: ug-ub=0 against the alternative Ha: ug-ub does not equal 0. Which of the following would be a Type I error?

Absorption rates into the body are important considerations when manufacturing a generic version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test H0: ug-ub=0 against the alternative Ha: ug-ub does not equal 0. Which of the following would be a Type I error?

A) Deciding that the absorption rates are different, when in fact they are not
B) Deciding that the absorption rates are the same, when in fact they are
C) Deciding that the absorption rates are different, when in fact they are the same
D) The researcher cannot make a Type I error, since he has run an experiment
E) Deciding that the absorption rates are the same, when in fact they are not

Answer: A

A philosophy professor wants to find out whether the mean age of men in his large lecture class is equal to the mean age of men in his class. After collecting data from a random sample of his students, the professor tests the hypothesis H0: u1-u1=0 against the alternative HA: u1-u2 does not equal 0. The P-value for the test was 0.003. Which is true?

A philosophy professor wants to find out whether the mean age of men in his large lecture class is equal to the mean age of men in his class. After collecting data from a random sample of his students, the professor tests the hypothesis H0: u1-u1=0 against the alternative HA: u1-u2 does not equal 0. The P-value for the test was 0.003. Which is true?

A) There is a 99.7% chance that another sample will give these results
B) It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women
C) There is a 0.3% chance that another sample will give these same results
D) There is a 0.3% chance that the mean ages for the men and women are equal
E) There is a 0.3% chance that the mean ages for the men and women are different

Answer: B

A professor was curious about her students' grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor's students?

A professor was curious about her students' grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor's students?

A) 3.01 +- 2.977(0.534/root 15)
B) 3.01+-2.97(0.534/root 14)
C) 3.01+-2.947(0.534/root 15)
D) 3.01+-2.947(0.534/root14)
E) 3.01+-2.576(0.534/root 15)

Answer: A

A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true?

A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true?

I. There is a 98% chance that eh mean hours per week spent studying by college students is between 13 and 17 hours
II. 98% of college students study between 13 and 17 hours a week
III. Students average between 13 and 17 hours per week studying on 98% of the weeks


A) none
B) I and III
C) II only
D) III only
E) I only

Answer: A

Which of the following is true about Student's t-models?

Which of the following is true about Student's t-models?

I. They are unimodal, symmetric and bell shaped
II. They have fatter tails than the Normal model
III. As the degrees of freedom increase, the t-models look more and more like the Normal



A) I, II, and III
B) I only
C) I and II
D) I and III
E) II and III

Answer: A

You could win a $1000 prize by tossing a coin in one of two games. To win Game A, you must get exactly 50% heads. To win Game B, you must get between 45% and 55% heads. Although which game you must play will be chosen randomly, then you may decide whether to toss the coin 20 times or 50 times. How many tosses would you choose to make?

You could win a $1000 prize by tossing a coin in one of two games. To win Game A, you must get exactly 50% heads. To win Game B, you must get between 45% and 55% heads. Although which game you must play will be chosen randomly, then you may decide whether to toss the coin 20 times or 50 times. How many tosses would you choose to make?

A) It does not matter.
B) 20 tosses for either game.
C) 50 tosses for either.
D) 20 tosses for A, 50 tosses for B.
E) 50 tosses for A, 20 tosses for B

Answer: D

The two samples whose statistics are given in the table are thought to come from populations with equal variances. What is the pooled estimate of the population standard deviation?

The two samples whose statistics are given in the table are thought to come from populations with equal variances. What is the pooled estimate of the population standard deviation?

A) 2.65
B) 7
C) 7.14
D) 7.22
E) 10

Answer: C

Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using an alpha=0.05. One students used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null. Which of these might have been their calculated value of t?

Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using an alpha=0.05. One students used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null. Which of these might have been their calculated value of t?

A) 1.22
B) 1.55
C) 1.88
D) 2.22
E) 2.66

Answer: C

Food inspectors need to estimate the level of contaminants in food products packaged at a certain factory. Initial tests were based on a small sample but now the inspectors double the sample size for a follow-up test. The main purpose of the larger sample is to

Food inspectors need to estimate the level of contaminants in food products packaged at a certain factory. Initial tests were based on a small sample but now the inspectors double the sample size for a follow-up test. The main purpose of the larger sample is to 

A) decrease the standard deviation of the sampling method
B) reduce confounding due to other variables
C) reduce response bias
D) decrease the variability in the population
E) reduce non-response bias

Answer: A

We want to know the mean winning score at the US open gold championship. An internet search gives us all the scores for the history of that tournament, and we create a 95% confidence interval based on a t-distribution. This procedure was not appropriate. Why?

We want to know the mean winning score at the US open gold championship. An internet search gives us all the scores for the history of that tournament, and we create a 95% confidence interval based on a t-distribution. This procedure was not appropriate. Why?

A) Since these are the best players in the world, the scores are probably skewed
B) The entire population of scores was gathered so there is no need to do inference
C) Tiger Woods' recent record-setting scores is probably an outlier
D) The population standard deviation is known, so we should have used a z-model
E) In big golf tournaments the players are not randomly selected

Answer: B

Investigators at an agricultural research facility randomly assigned equal numbers of chickens to be housed in two rooms. In group of chickens experienced normal day/night cycles, while in the other room lights were left on 24 hours a day to see if those chickens would lay more eggs. After collecting data for several days the researchers tested the hypothesis H0: u1-u2=0 against the one-tail alternative and found P-0.22. Which is true?

Investigators at an agricultural research facility randomly assigned equal numbers of chickens to be housed in two rooms. In group of chickens experienced normal day/night cycles, while in the other room lights were left on 24 hours a day to see if those chickens would lay more eggs. After collecting data for several days the researchers tested the hypothesis H0: u1-u2=0 against the one-tail alternative and found P-0.22. Which is true?

A) The chickens in the lighted room averaged 0.22 more eggs per day
B) There's a 22% chance that chickens housed in a lighted room produce more eggs.
C) There's a 22% chance that there's really no difference in egg production D) There's a 22% chance another experiment will give these same results
E) None of these

Answer: E

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and a standard deviation of 1.88gm. Assuming these squirrels can be considered a random sample of all red squirrels which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels?

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and a standard deviation of 1.88gm. Assuming these squirrels can be considered a random sample of all red squirrels which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels?

A) 12.32+- 1.96(1.88/root10)
B) 12.32=-2.228(1.88/root10)
C) 12.32+-2.262(1.88/root10)
D) 12.32+-2.228(1.88/root9)
E) 12.32+-2.268(1.88/root9)

Answer: C

A random sample of 120 college seniors found that 30% of them had been offered jobs. What is the standard error of the sample proportion?

A random sample of 120 college seniors found that 30% of them had been offered jobs. What is the standard error of the sample proportion?

A) 0.028
B) 0.042
C) 0.046
D) 0.082
E) 0.458

Answer: B

A company checking the productivity of its assembly line monitored a random sample of workers for several days. They found that a 95% confidence interval for the mean number of items produced daily by each worker was (23, 27). Which is true?

A company checking the productivity of its assembly line monitored a random sample of workers for several days. They found that a 95% confidence interval for the mean number of items produced daily by each worker was (23, 27). Which is true?

A) 95% of the workers sampled produced between 23 and 37 items a day.
B) 95% of all the workers average between 23 to 27 items on 95% of the days.
C) Workers produce an average of 23 to 27 items on 95% of the days.
D) 95% of samples would show mean production between 23 and 27 items a day.
E) We're 95% sure that the mean daily worker output is between 23 and 27 items.

Answer: E

Which statement correctly compares t-distributions to the Normal distribution?

Which statement correctly compares t-distributions to the Normal distribution?

I. t distributions are also mound shaped and symmetric
II. t distributions are more spread out than the normal distribution
III. As degrees of freedom increase, the variance of t distributions becomes smaller


A) I only
B) II only
C) I and II only
D) I and III only
E) I, II and III

Answer: C

Facts about Least-Squares Regression

Facts about Least-Squares Regression

1. Distinguishing between explanatory and response variables is essential in regression.
2. There is a close connection between correlation and the LSRL's slope.
b=r(sy/Sx)
b and r are either positive or both negative.
3. The LSRL of y on x always passes through the point (x bar, y bar)
4. Correlation, r, describes strength and direction of a linear relationship. r^2, the coefficient of determination, is the fraction of the variation in y values that is explained by the LSRL of y on x.

What is the coefficient of determination?

What is the coefficient of determination?

Answer: the fraction of the variation in y that is explained by the least-squares regression of y on x

A residual plot is a graphical measure of how well the LSRL fits the data. The numerical measure of that same fit is

A residual plot is a graphical measure of how well the LSRL fits the data. The numerical measure of that same fit is

Answer: r^2

What are the two important aspects of a residual plot?

What are the two important aspects of a residual plot?

Answer:

1. The plot should show no obvious pattern.
2. The residuals should not be relatively small in size.

What is a residual?

What is a residual?

Answer: the difference between an observed value of the response variable and the value predicted by the regression line

What are residuals?

What are residuals?

Answer: the vertical distances from a scatter plot's points to the least-squares regression line

The predicted response will usually

The predicted response will usually

Answer: not be exactly the the same as the actual observed response.

Why is y with hat used in the LSRL equation?

Why is y with hat used in the LSRL equation?

Answer: to emphasize that the line gives a predicted response for any x.

Every LSRL passes through the point

Every LSRL passes through the point

Answer: (x with bar, y with bar)

The LSRL equation is

The LSRL equation is

Answer:

y with hat= a+bx
where b= r(Sy/Sx)
and a= y with bar minus b(x with bar)

What is the Least Squares Regression Line Equation?

What is the Least Squares Regression Line Equation?

Answer: Given an explanatory variable 'x' and a response variable 'y,' calculate their means, their standard deviations, and their correlation.

What is the Least Squares Regression Line?

What is the Least Squares Regression Line?

Answer: The LSRL of y on x is the line that makes the sum of the squared vertical distances of the data points from the line as small as possible

Because the line predicts y from x, the prediction errors are made in the

Because the line predicts y from x, the prediction errors are made in the

Answer: y direction, the vertical direction

What is the Least Squares Method?

What is the Least Squares Method?

Answer: making the vertical distance of the points from the line as small as possible

What does a good regression line do?

What does a good regression line do?

Answer: makes the vertical distance of the points from the line as small as possible

What is extrapolation?

What is extrapolation?

Answer: The use of a regression line for prediction outside the range of explanatory variable values used to obtain the line

Why is a regression line used?

Why is a regression line used?

Answer: to predict a value for 'y' for a given value of 'x'

What is a regression line?

What is a regression line?

Answer:

- A line that describes how a response variable 'y' changes as an explanatory variable 'x' changes.
- a model for the data

A regression line summarizes the relationship between two variables, but only in the setting when

A regression line summarizes the relationship between two variables, but only in the setting when

Answer: one variable helps explain or predict the other

What does a regression line do?

What does a regression line do?

Answer: summarizes the relationship between two variables

When a scatter plot shows a linear relationship, its overall pattern can be summarized by

When a scatter plot shows a linear relationship, its overall pattern can be summarized by

Answer: drawing a line on the scatter plot

How do outliers appear in a Normal Probability Plot?

How do outliers appear in a Normal Probability Plot?

Answer: as points far away from the plot's overall pattern

What indicates a non-normal pattern in a Normal Probability Plot?

What indicates a non-normal pattern in a Normal Probability Plot?

Answer: Deviations from a straight line

What indicates that the data is normal in a Normal Probability Plot?

What indicates that the data is normal in a Normal Probability Plot?

Answer: If the points lie close to a straight line.