STA2023 Exam practice questions

Suppose our p-value is .044. What will our conclusion be at alpha levels of .10, .05, and .01?

b) We will reject Ho at alpha=.10 or .05, but not at alpha=.01

A survey was conducted to get an estimate of the proportion of smokers among the graduate students. Report says 38% of them are smokers. Chatterjee doubts the result and thinks that the actual proportion is much less than this. He takes a sample of 25 students to test the survey result. Let p be the proportion of smokers among the graduate students.

c) Ho: p=.38 versus Ha: p< .38.

Suppose you conduct hypothesis test for the population proportion and your p-value is .184. Given a 0.10 level of significance, which of the following should be your conclusion?

d) Fail to reject HO

A random sample of married people were asked "Would you remarry your spouse if you were given the opportunity for a second time?"; Of the 150 people surveyed, 127 of them said that they would do so. Find a 95% confidence interval for the proportion of married people who would remarry their spouse.

d) 0.847 ± 0.058

Refer to question 38, but this time suppose we take a random sample of 16 males from Alachua County. Approximately, what is the probability that the sample mean of our 16 subjects is bigger than 193 lbs?

d) Cannot say from the information provided

If you increase the sample size and confidence level at the same time, what will happen to the length of your confidence interval?

d) cannot be determined from the given information

What is the probability that our sample will have more than 70% of people prefer chocolate ice cream?

b. 0.0005

What should be the value of z used in a 93% confidence interval?

c) 1.81

When are p-values negative?

e) never

Questions 16-19 A certain brand of jelly beans are made so that each package of these jelly beans contains about the same number of beans. The filling procedure is not perfect, however. The packages are filled with an average of 375 jelly beans, but the number going into each bag is normally distributed with a standard deviation of 8. Yesterday, Jane went to the store and purchased four of these packages in preparation for a Spring party. Jane was curious, and she counted the number of jelly beans in these packages. She determined that her four bags contained an average of 382 jelly beans. 16. In the above scenario, which of the following is a parameter? 17. If you went to the store and purchased six bags of this brand of jelly beans, what is the probability that the average number of jelly beans in your bags is less than 373? 18. Why can we use the Z table to compute the probability in the previous question? 19. According to the central limit theorem, what is the standard deviation of the sampling distribution of the sample mean?

16. c) The average number of jelly beans in all packages made, which is 375. 17. a) .2709 18. c) because the distribution of jelly beans is Normal 19. c) The standard deviation of the population divided by the square root of the sample size

Questions 20-23 Researchers are concerned about the impact of students working while they are enrolled in classes, and they'd like to know if students work too much and therefore are spending less time on their classes than they should be. First, the researchers need to find out, on average, how many hours a week students are working. They know from previous studies that the standard deviation of this variable is about 5 hours. 20. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample? 21. Suppose that this confidence interval was (6.82, 7.38). Which of these is a valid interpretation of this confidence interval? 22. We have 95% confidence in our interval, instead of 100%, because we need to account for the fact that: 23. The researchers are not satisfied with their confidence interval and want to do another study to find a shorter confidence interval. What should they change to ensure they find a shorter confidence interval?

20. b) (6.41, 7.79) 21. d) We are 95% confident that the average number of hours worked by all UF students is between 6.82 and 7.38 hours. 22. b) we have a sample, and not the whole population. 23. c) They should decrease their confidence level but increase their sample size.

Questions 26-27 Recent studies have shown that 20% of Americans are fit the medical definition of obese. A nutrition professor would like to study the percentage of students on campus that are obese. Suppose that the percentage of students that are obese at UF is the same as the percentage of Americans. Let X equal the number of students that are obese. 26. For the sample of 100 teenagers, what is the sampling distribution of the sample proportion? 27. Suppose that she took a sample of 100 teenagers. What is the probability that the sample proportion is greater than 0.24?

26. c.) p ˆ ~N(0.2, 0.04) 27. b.) 0.1587

Questions 29- 30 Suppose 20 donors come to a blood drive. Assume that the blood donors are not related in any way, so that we can consider them independent. The probability that the donor is O- blood is 0.06, which is constant from donor to donor. Let X = the number of donors that have O- blood. 29.For the sample of 100 donors, what is the sampling distribution of the sample proportion? 30. For the sample of 300 donors, what is the sampling distribution of the sample proportion?

29. d.) Can not be determined 30. c.) p ˆ ~Normal(0.06, 0.013711)

Questions 48-50: Suppose we are interested in finding a 95% confidence interval for the mean SAT Verbal score of students at a certain high school. (Assume that these scores are normally distributed.) Five students are sampled, and their SAT Verbal scores are 560, 500, 470, 660, and 640. 48. What is the standard error of the sample mean? 49. What is the 95% confidence interval for the population mean? 50. The method used to calculate the confidence interval in Question 49 assumes which one of the following?

48. b) 37.36 49. a) (462.3, 669.7) 50. c) The population has an approximately normal distribution.

Questions 52-53 We know that 65% of all Americans prefer chocolate over vanilla ice cream. Suppose that 1000 people were randomly selected. 52. The standard error of the sample proportion is 53. The Sampling Distribution of the sample proportion is

52. b. 0.01508 53. b. Normal( 0.65, 0.01508)

Questions 59 - 61. Commercial fishermen working in certain parts of the Atlantic Ocean sometimes find their efforts being hindered by the presence of whales. Ideally, they would like to scare away the whales without frightening the fish. One of the strategies being experimented with is to transmit underwater the sounds of a killer whale. On the 52 occasions that that technique has been tried, it worked 24 times (that is, the whales left the area immediately). Experience has shown, though, that 40% of all whales sighted near fishing boats leave on their own accord, anyway, probably just to get away from the noise of the boat. 59. What would a reasonable hypothesis test be: 60. Suppose you want to test Ho: p=0.4 versus Ha: p > 0.40 at the 0.05 level of significance. What would your conclusion be? 61. The following is a list of assumptions that you might want to check before proceeding to a significance test for p ˆ . I. The data is obtained from a random sample II. The variable is categorical III. The variable is quantitative IV. The population size is large V. The population is normally distributed VI. The sample size is sufficiently large VII. The sampling distribution of p ˆ is approximately normal What assumptions must be satisfied in order to be able to conduct a significance test for p ˆ ?

59. d) Ho: p=0.4 versus Ha: p > 0.40 60. d) Fail to reject Ho. 61. b) I, II, and VII

Questions 34 Researchers are designing a study to determine if the age of the victim is a factor in reported scams. The researchers are testing to determine if more than half of all reported scams victimize the elderly. They randomly sample 350 reported scams over the past 10 years from the Better Business Bureau archives, and note that, for 287of them, the victim is over 65 years old. 34. Match the following symbols with the correct number on the right: _____ p a) 0.50 _____ p-hat b) 65 _____ p0 c) 287 _____ x d) 350 _____ n e) 0.820 f) 0.816 g) unknown

G. --- p E. --- p^ A --- p0 C. ---- x D --- n

Suppose that the probability that Joakim Noah, a former UF basketball player, makes a free throw is p = 0.75. Now suppose that he shoots 100 free throws over the course of a basketball season (sample of 100 independent free throws). Find the approximate probability that Joakim makes less than 65% of his free throws during the course of the season.

a) 0.0104

A 95% confidence interval for the mean number of televisions per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false. a. The probability that is between 1.15 and 4.20 is .95. b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20. c. 95% of all samples should have x-bars between 1.15 and 4.20. d. 95% of all American households have between 1.15 and 4.20 televisions. e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean. f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.

a) F b) T c) F d) F e) T f) T

For each of the following situations, can we use the Z table to compute probabilities (T/F): _____ a. Weights of adults are approximately Normally distributed with mean 150 lbs and stdev 25 lbs. We want to know the probability that a randomly selected person weights more than 200 pounds. _____ b. Weights of adults are approximately Normally distributed with mean 150 lbs and stdev 25 lbs. We want to know the probability that the average weight of 10 randomly selected people is more than 200 pounds. _____ c. Weights of adults are approximately Normally distributed with mean 150 lbs and stdev 25 lbs. We want to know the probability that the average weight of 50 randomly selected people is more than 200 pounds. _____ d. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want to know the probability that a randomly selected employee makes more than $50,000. _____ e. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want to know the probability that the average of ten randomly selected employees is more than $50,000. _____ f. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want to know the probability that the average of fifty randomly selected employees is more than $50,000. _____ g. A club has 50 members, 10 of which think the president should be deposed. What is the probability that, if we select 20 members at random, 18% or more in our sample think the president should be deposed? _____ h. A club has 5000 members, 1000 of which think the president should be deposed. What is the probability that, if we select 91 members at random,20% or more in our sample think the president should be deposed?

a) T b) T c) T d) F e) F f) T g) F h) T

Which of the following is true about p-values?

a) a p-value must be between 0 and 1.

Decreasing the sample size, while holding the confidence level the same, will do what to the length of your confidence interval?

a) make it bigger

For the sample of 300 donors, what is the probability that the sample proportion is greater than 0.10?

a.) 0.0019

The null hypothesis Ho: p=.5 against the alternative Ha: p>.5 was rejected at level alpha=0.01.Nate wants to know what the test will result at level alpha=0.10.what will be the result if Nate performs the test at level alpha=0.10?

a.) Reject Ho

The executives at Sandbachian, Inc., having recently solved their widget crisis, have another problem with one of their products. Many cities are sending complaints that their manhole covers are defective and people are falling into the sewers. The workers took a random sample of 800 manhole covers and found that 40 of them were defective. What is the 95% CI for p, the true proportion of defective manhole covers, based on this sample?

b) (.035, .065)

Suppose we are interested in finding a 95% confidence interval for the proportion p of UF undergraduate students who are from the state of Florida. We take a random sample of 20 students, and we find that 17 of them are from Florida. What should we compute as our 95% confidence interval for p?

b) (.629, .954)

38. Suppose the average weight for adult males (age 18 or older) in Alachua County is 190 lbs with a standard deviation of 20. Now suppose we take a random sample of 143 adult males (age 18 or older) in Alachua County. Approximately, what is the probability that the sample mean of our 143 subjects is bigger than 193 lbs?

b) 0.0367

Suppose that we wanted to estimate the true average number of eggs a queen bee lays with 95% confidence. The margin of error we are willing to accept is 0.5. Suppose we also know that s is about 10. What sample size should we use?

b) 1537

For a test with the null hypothesis Ho: p = 0.5 vs. the alternative Ha: p > 0.5, the null hypothesis was not rejected at level alpha=.05.Das wants to perform the same test at level alpha=.025.What conclusion will he make after doing the test?

b) Fail to Reject H0.

You suspect that the most popular color for a Nalgene water bottle is blue, but you would like to verify that. For this purpose you decide to estimate what proportion of the Nalgene water bottles used at UF are blue. Describe what the population is, and state how you plan to find p ˆ . In answering this question, keep in mind that a single student may have more than one water bottle (possibly of different colors), or none at all.

b) The population is all Nalgene water bottles used at UF. (Number of blue Nalgene bottles in the sample) / (Total number of Nalgene bottles in the sample) = p^

Decreasing the confidence level, while holding the sample size the same, will do what to the length of your confidence interval?

b) make it smaller

Suppose the probability that Barry Bonds, a famous baseball player, gets a hit in a given at bat is p = 0.3. If Barry has 400 at bats in a single season (sample of 400 independent at bats), what is the mean and standard error of the sampling distribution p-hat (the sample proportion of hits per at bat)?

b) mean = 0.3, standard error = 0.0229

You would like to estimate the proportion of "regular users of vitamins" in a large population. In order to find a confidence interval for the proportion,

b) we must assume that we have a random sample from some binary population where np> 15 and n(1-p)> 15

The executives at Sandbachian, Inc. having recently solved their widget crises, have another major problem with one of their products. Many cities are sending complaints that their manhole covers are defective and people are falling into the sewers. Sandbachian, Inc. is pretty sure that only 4% of their manhole covers are defective, but they would like to do a study to confirm this number. They are hoping to construct a 95% confidence interval to get within 0.01 of the true proportion of defective manhole covers. How many manhole covers need to be tested?

b. 1476

Parameters and statistics

b. Describe the population and the sample, respectively.

Why do we use inferential statistics?

b. to make informed predictions about parameters we don't know

A waiter believes that his tips from various customers have a slightly right skewed distribution with a mean of 10 dollars and a standard deviation of 2.50 dollars. What is the probability that the average of 35 customers will be more than 13 dollars?

b.) almost zero

Which of the following statements about small-sample and large-sample confidence intervals for proportions are true? I. The large-sample confidence interval formula for proportions is valid if n𝑝̂≥ 15 and n(1-𝑝̂) ≥ 15. II. Large-sample confidence intervals always contain the true parameter value, whereas small-sample confidence intervals may not. III. We form small-sample confidence intervals by using the large-sample formula after adding 4 successes and 4 failures.

c) I only

A political poll of Americans was conducted to investigate their opinions on gun control. Each person was asked if they were in favor of gun control or not in favor of gun control - no respondents were removed from the results. The survey found that 25% of people contacted were not in favor of gun control laws. These results were accurate to within 3 percentage points, with 95% confidence. Which of the following is NOT CORRECT?

c) In approximately 95% of polls on this issue, the confidence interval will include the sample proportion.

Suppose our p-value is .02. Which of the following is true?

c) We will reject H0 at alpha = 0.05

Which of the following is a property of the Sampling Distribution of x bar?

c) the mean of the sampling distribution of x bar is mu the population mean.

You take a random sample from some population and form a 96% confidence interval for the population mean, mu, Which quantity is guaranteed to be in the interval you form?

c) x bar

Let x1, x2, ..., x50 be independent observations from a distribution X which is not normal. Suppose it is known that the mean of this distribution is 48 and the standard deviation is 5. What can we say about the sample mean x-bar?

c) x-bar is distributed approximately normal with mean 48 and standard error 5/√(50)

We are doing an experiment where we record the number of heads we get when we flip an unbiased coin many times. For what sample sizes below would the sampling distribution of the sample proportion be approximately normally distributed?

c. 50

When doing a significance test, a student gets a p-value of 0.003. This means that: I. Assuming Ho were true, this sample's results were an unlikely event. II. 99.97% of samples should give results which fall in this interval. III. We reject Ho at any reasonable alpha level.

c. I and III

A sample of size 45 is drawn from a slightly skewed distribution. What is the approximate shape of the sampling distribution?

c. Normal Distribution

An auto insurance company has 32000 clients. Out of all of the clients, 5% have submitted a a claim in the past year. They take a sample of 3,200 clients. What is the sampling distribution

c.) p ˆ ~N(0.05,0.003852)

A null hypothesis was rejected at level alpha=0.10.What will be the result of the test at level alpha=0.05?

c.) No conclusion can be made

"What are the possible values of x-bar for all samples of a given n from this population?" To answer this question, we would need to look at the:

d. sampling distribution