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2023 Exam 250713RR Sampling Distributions and Estimation Hypothesis Testing Questions 1 to 20 Select the best answer to each question

Exam: 250713RR – Sampling Distributions and Estimation; Hypothesis Testing

Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. Determine the power for the following test of hypothesis.

H : μ = 950 vs. H : μ ≠ 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.

01

0.4938

0.3465

0.6535

0.5062

2. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance?

We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75 pounds per person per year.

We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.

We can conclude that we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.

We can conclude that the average cottage cheese consumption in America isn’t 2.6 pounds per person per year.

3. In sampling without replacement from a population of 900, it’s found that the standard error of the mean, , is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?

500

400

600

200

4. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use α = 0.05 and assume a normally distributed population.

No, because the test statistic is –1.85 and falls in the rejection region.

Yes, because the sample mean of 9.25 is below 9.5.

Yes, because the test statistic is greater than –1.645.

No, because the test statistic falls in the acceptance region.

5. Nondirectional assertions lead only to _______-tail tests.

two

right

one

left

6. In the statement of a null hypothesis, you would likely find which of the following terms?

<

=

>

≠

7. What sample size is required from a very large population to estimate a population proportion within

0.05 with 95% confidence? Don’t assume any particular value for p.

38

271

385

767

8. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven’t really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?

H : p = 0.10 and H : p ≠ 0.10

1

H0: p > 0.10 and H1: p ≤ 0.10

H : p ≥ 0.10 and H : p < 0.10

1

H0: p ≤ 0.10 and H1: p > 0.10

9. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?

15

8

4

16

10. Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.

N = 2500; n = 75

N = 1500; n = 300

N = 150; n = 25

N = 15,000; n = 1,000

11. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she’ll perform _______-tail testing of a _______.

two, mean

two, proportion

one, proportion

one, mean

12. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?

20.3, 95%

18.3, 0.95

20.3, 0.95

18.3, 95%

13. Which of the following statements about p-value testing is true?

P-value testing uses a predetermined level of significance.

The p represents sample proportion. C. The p-value is the lowest significance level at which you should reject H .

0

D. P-value testing applies only to one-tail tests.

14. If the level of significance (α) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?

A. 0.005

B. 0.995

0.050

0.9975

15. What is the rejection region for a two-tailed test when α = 0.05?

|z | > 1.96

|z | > 1.645

|z | > 2.575

z > 2.575

16. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?

Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.

You can use t all the time, but for n ≥ 30 there is no need, because the results are almost identical if you use t or z.

The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.

Use t when the sample size is small, and the resulting confidence interval will be narrower.

17. In a simple random sample from a population of several hundred that’s approximately normally distributed, the following data values were collected.

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the population mean is somewhere between

73.36 and 88.24.

65.33 and 95.33.

69.15 and 92.45.

71.36 and 90.24.

18. In a criminal trial, a Type II error is made when a/an

innocent person is acquitted.

innocent person is convicted.

guilty defendant is convicted.

guilty defendant is acquitted.

19. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm’s employees?

4

30

3

2.5

20. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?

The researcher should use the z-test because the sample size is less than 30.

The t-test should be used because the sample size is small.

The t-test should be used because α and μ are unknown.

The researcher should use the z-test because the population is assumed to be normally distributed.

Exam: 250714RR – Inferences and Linear Regression

1. Another name for the residual term in a regression equation is

homoscedasticity.

random error.

pooled variances.

residual analysis.

2. An indication of no linear relationship between two variables would be a coefficient of

correlation equal to −1.

determination equal to −1.

determination equal to 1.

correlation of 0.

3. The object on which the response and factors are observed is called

factor level.

experimental unit.

treatments.

factors.

4. In using the ANOVA models, the assumptions made about the data are

the population variances are equal.

the samples are independent.

all 3 assumptions made here about the data.

the population distributions are normal.

5. Which of the following statements are true regarding the simple linear regression model y = β + β x +

i01 i ε ? i

y is a value of the dependent variable (y) and x is a value of the independent variable (x). ii

β0 is the slope of the regression line. C. β is the y-intercept of the regression line. 1

D. εi is a nonrandom error.

6. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

NMEANMEDIANTRMEANSTDEV SEMEAN

FEMALES3323.9120.0023.389.771.70

MALES3828.8728.5028.449.671.57

What is the value of the test statistic (Z score)?

1.64

−4.96

2.32

−2.14

7. A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: yˆ = 80,000 + 5x. This implies that an increase of _______ in advertising is expected to result in an increase of _______ in sales.

$1, $5,000

$1, $5

$1, $80,005

$5, $5,000

8. A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that

0.025 > p-value > 0.01.

0.05 > p-value > 0.025.

p-value < 0.01.

0.10 > p-value > 0.05.

9. In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference

x̄ − x̄ if the

12

populations are at least normally distributed with equal variances.

sizes are both greater than 30.

populations are nonnormal with unequal variances.

ample sizes are both large.

10. Lily Energy Systems manufacturer’s wood-burning heaters and fireplace inserts. One of its systems has an electric blower, which is thermostatically controlled. The blower is designed to automatically turn on when the temperature in the stove reaches 125°F and turn off at 85°F. Complaints from customers indicate that the thermostat control is not working properly. The company feels that the thermostat is acceptable if the variance in the cutoff temperature is less than or equal to 175. The company takes a sample of 24 thermostats and finds that the variance equals 289. The calculated chi-square test statistic and the table value for a 0.05 significance level are

38.076, 38.99.

37.983, 35.172.

35.172, 38.99.

37.983, 38.076.

11. In testing a population variance or constructing a confidence interval for the population variance, an essential assumption is that

the population is normally distributed.

expected frequencies equal or exceed 5.

the population is uniformly distributed.

sample size exceeds 30.

12. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) is

8.45.

5.89.

27.67.

14.62.

13. Consider the following data values of variables x and y.

x42643

y53765

Find the least squares regression line.

−1.045 + 0.932x

1.122 + 1.073x

1.659 + 0.932x

21.206 + 1.073x

14. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

N MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES 3323.9120.0023.389.771.70

MALES3828.8728.5028.449.671.57

What is the standard error of the statistic between the two means?

1.635

0.897

2.314

4.96

15. A “best-fit” mathematical equation for the values of two variables, x and y, is called

errors of prediction.

regression analysis.

correlation analysis.

scatter diagram.

16. In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of

0.10.

0.20.

0.05.

0.90.

17. The vertical distances between observed and predicted values of y are called

least square lines.

scatterplots.

errors of prediction.

methods of least squares.

18. A balanced experiment requires that

an equal number of persons or test units receives each treatment.

at least two treatment groups be used.

the number of treatments equals the number of samples.

at least one sample equal size is 30.

19. A left-tail area in the chi-square distribution equals 0.95. For df = 10, the table value equals

18.307.

3.940.

20.483.

15.987.

20. With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution.

binomial

t-

Poisson

normal

Exam: 250712RR – Probability

Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. In the binomial probability distribution, p stands for the

probability of success in any given trial.

probability of failure in any given trial.

number of successes.

number of trials.

2. Which of the following is a discrete random variable?

The weight of football players in the NFL

The number of three-point shots completed in a college basketball game

The average daily consumption of water in a householdD. The time required to drive from Dallas to Denver

3. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. The standard deviation is 6. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?

0.475

0.239

0.342

0.136

4. What is the value of ?

336

1.6

6720

56

5. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard deviation is _______ burgers.

6

3

18

9

6. Assume that an event A contains 10 observations and event B contains 15 observations. If the intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?

22

0

10

28

7. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Let A be the event “shaggy and brown-haired.” Compute P(Ac).

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

0.49

0.51

0.36

0.77

8. If event A and event B are mutually exclusive, P(A or B) =

P(A + B).

P(A) + P(B) – P(A and B).

P(A) + P(B).

P(A) – P(B).

9. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times. Assume each repetition is independent of the others. What is the probability of three successes?

0.055

1.14

0.238

0.762

A continuous probability distribution represents a random variable

having an infinite number of outcomes that may assume any number of values within an interval.

that’s best described in a histogram.

that has a definite probability for the occurrence of a given integer.

having outcomes that occur in counting numbers.

11. Which of the following is correct concerning the Poisson distribution?

The event being studied is restricted to a given span of time, space, or distance.

The mean is usually larger than the variance.

The mean is usually smaller than the variance.

Each event being studied must be statistically dependent on the previous event.

Protestant Catholic Jewish Other

Democrat 0.35 0.10 0.03 0.02

Republican 0.27 0.09 0.02 0.01

Independent 0.05 0.03 0.02 0.01

12. The table above gives the probabilities of combinations of religion and political parties in a city in the United States. What is the probability that a randomly selected person will be a Protestant and at the same time be a Democrat or a Republican?

0.62

0.89

0.67

0.35

13. A basketball team at a university is composed of ten players. The team is made up of players who play the position of either guard, forward, or center. Four of the ten are guards, four are forwards, and two are centers. The numbers that the players wear on their shirts are 1, 2, 3, and 4 for the guards; 5, 6, 7, and 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. The events are defined as follows:

Let A be the event that the player selected has a number from 1 to 8.

Let B be the event that the player selected is a guard.

Let C be the event that the player selected is a forward.

Let D be the event that the player selected is a starter.

Let E be the event that the player selected is a center.

Calculate P(C).

0.50

0.80

0.40

0.20

14. Each football game begins with a coin toss in the presence of the captains from the two opposing teams. (The winner of the toss has the choice of goals or of kicking or receiving the first kickoff.) A particular football team is scheduled to play 10 games this season. Let x = the number of coin tosses that the team captain wins during the season. Using the appropriate table in your textbook, solve for P(4 ≤ x ≤ 8).

0.246

0.817

0.171

0.377

15. Approximately how much of the total area under the normal curve will be in the interval spanning 2 standard deviations on either side of the mean?

50%

68.3%

95.5%

99.7%

16. If the probability that an event will happen is 0.3, what is the probability of the event’s complement?

0.1

0.7

1.0

0.3

17. The area under the normal curve extending to the right from the midpoint to z is 0.17. Using the standard normal table on the textbook’s back endsheet, identify the relevant z value.

–0.0675

0.44

0.0675

0.4554

18. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In this study, x is a

dependent event.

joint probability.

continuous quantitative variable.

discrete random variable.

19. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it’s short-haired?

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

0.0306

0.222

0.06

0.105

20. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?

Events A and B are exhaustive.

On a Venn diagram, event A would overlap event B.

Events A and B are mutually exclusive.

On a Venn diagram, event B would contain event A.

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