In a certain town 60% of the households own mutual funds, 40% own individual stocks, and 20% own both mutual funds and individual stocks.

1. The proportion of households that own mutual funds but not individual stocks is a. 20%. b. 30%. c. 40%. d. 50%.

2. The proportion of households that own neither mutual funds nor individual stocks is a. 20%. b. 30%. c. 40%. d. 50%.

3. The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is a. 40%. b. 60%. c. 80%. d. 100%.

Use the following to answer questions 4-5.

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent.

4. The probability that it lands on red neither time is a. 0.2244. b. 0.2770. c. 0.4488. d. 0.9474.

5. The probability that it lands once on red and once on black is a. 0.2244. b. 0.2770. c. 0.4488. d. 0.9474.

6. In an instant lottery, your chances of winning are 0.2. If you play the lottery five times and outcomes are independent, the probability that you win at most once is a. 0.0819. b. 0.2. c. 0.4096. d. 0.7373.

7. In an instant lottery, your chances of winning are 0.2. If you play the lottery five times and outcomes are independent, the probability that you win all five times is a. 0.6723. b. 0.3277. c. 0.04. d. 0.00032.

Use the following to answer questions 8-10.

A survey asks a random sample of 2500 adults in Ohio if they support an increase in the state sales tax from 5.25% to 5.50%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 30% of all adults in Ohio support the increase.

8. The mean of X is a. 30. b. 525. c. 750. d. 1750.

9. The standard deviation of X is a. 22.91. b. 27.39. c. 5255. d. 750.

10. The probability that X is at least 800 is a. less than 0.0001. b. about 0.015. c. 0.025. d. 0.05.

11. The upper 0.01 critical value of the standard normal distribution is a. 1.645. b. 2.054. c. 2.326. d. 2.576.

Use the following to answer question 12.

An agricultural researcher plants 100 plots with a new variety of corn. The average yield for these plots is bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean and standard deviation bushels per acre. 12. A 90% confidence interval for is a. 150 2.00. b. 150 3.29. c. 150 3.92. d. 150 32.90.

Use the following to answer question 13.

You measure the weights of a random sample of 25 male runners. The same mean is kilograms (kg).

13. Suppose that the mean weights of male runners follow a normal distribution with unknown mean and standard deviation kg. A 95% confidence internal for is a. 59.61 to 60.39. b. 59 to 61. c. 58.04 to 61.96. d. 50.2 to 69.8.

Use the following to answer questions 14-15.

The heights of 15-year-old American boys, in inches, are normally distributed with mean and standard deviation I select a simple random sample of four 15-year-old American boys and measure their heights. The four heights, in inches, are

63 69 62 66

14. Based on these data, a 99% confidence interval for, in inches, is a. 65.00 1.55. b. 65.00 2.35. c. 65.00 3.09. d. 65.00 4.07.

15. If I wanted the margin of error for the 99% confidence interval to be 1 inch, I should select a simple random sample of size a. 2. b. 7. c. 16. d. 39.

16. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a. a statement of "no effect" or "no difference." b. the probability of observing the data you actually obtained. c. a statement that the data are all 0. d. 0.05.

17. In their advertisements, the manufacturers of a diet pill would like to claim that taken daily, their pill will produce a mean weight loss of more than 10 pounds in one month. In order to determine if this is a valid claim, they hire an independent testing agency, which then selects 25 people to take the pill daily for a month. The agency should be testing the null hypothesis and the alternative hypothesis a. b. c. d.

18. Suppose we are testing the null hypothesis and the alternative for a normal population with A random sample of nine observations are drawn from the population and we find the sample mean of these observations is . The P-value is closest to a. 0.0668. b. 0.1336. c. .0332. d. .3085.

19. The mean area of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, , for are a. b. c. d. cannot be specified without knowing the size of the sample used by the engineer.

20. Is the mean height for all adult American males between the ages of 18 and 21 now over 6 feet? If the population of all adult American males between the ages of 18 and 21 has mean height of feet and standard deviation feet, to answer this question one would test which of the following null and alternative hypotheses? a. b. c. d. assuming our sample size is n.

21. In assessing the validity of any test of hypotheses, it is good practice to a. examine the probability model that serves as a basis for the test by using exploratory data analysis on the data. b. determine exactly how the study was conducted. c. determine what assumptions the researchers made. d. all of the above.

22. In studies of worker productivity, it has been noticed that any change in the work environment together with knowledge that a study is underway will produce a short-term increase in productivity. This is known as a. statistical significance. b. the Hawthorne effect. c. practical significance. d. a critical value.

23. A Type II error is a. rejecting the null hypothesis when it is true. b. accepting the null hypothesis when it is false. c. incorrectly specifying the null hypothesis. d. incorrectly specifying the alternative hypothesis.

Use the following to answer questions 24-25.

A researcher plans to conduct a test of hypotheses at the significance level. She designs her study to have a power of 0.80 at a particular alternative value of the parameter of interest.

24. The probability that the researcher will commit a Type I error is a. 0.05. b. 0.20. c. 0.80. d. equal to the P-value and cannot be determined until the data have been collected.

25. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power is a. 0.05. b. 0.20. c. 0.80. d. equal to the 1 - (P-value) and cannot be determined until the data have been collected.

Use the following to answer questions 26-28.

A SRS of 20 third grade children is selected in Chicago and each is given a test to measure his or her reading ability. In the sample, the mean score is 64 points and the standard deviation is 12 points.

26. The standard error of the mean is a. 14.31. b. 7.20. c. 2.68. d. 0.60.

27. We are interested in a 95% confidence interval for the population mean score. The margin of error associated with the confidence interval is a. 2.68 points. b. 4.64 points. c. 5.62 points. d. 6.84 points.

28. A 90% confidence interval for the population mean score based on these data is a. points. b. points. c. points. d. points.

29. The appraised values of three recently sold houses in the Columbus area are (in thousands of dollars) 160, 215, and 195. The standard error of the mean of these three appraised values is a. 190.00. b. 27.84. c. 22.73. d. 16.07.

30. The one-sample t statistic from a sample of n = 19 observations for the two-sided test of

has the value t = 1.93. Based on this information a. we would reject the null hypothesis at b. 0.025

Use the following to answer questions 31-35.

A food company is developing a new breakfast drink, and their market analysts are currently working on preliminary taste-testing studies. To help with their marketing strategy, they were first interested in whether preference for the new product was related to a person's gender. There were 100 male and 100 female volunteers available for the taste test. Both the males and females tasted the product and rated the flavor on a scale of 1 to 10, 1 being "very unpleasant" and 10 being "very pleasant." The mean rating for males was with a standard deviation The mean rating for females was with a standard deviation Let and represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations.

31. A 90% confidence interval for is (use the conservative value for the degrees of freedom) a. b. c. d.

32. Suppose the researcher had wished to test the hypotheses

The numerical value of the two-sample t statistic is a. 2.00. b. 2.40. c. 3.25. d. 9.60.

33. Suppose the researcher had wished to test the hypotheses

The P-value for the test is (use the conservative value for the degrees of freedom) a. larger than 0.10. b. between 0.10 and 0.05. c. between 0.05 and 0.01. d. below 0.01.

34. Which of the following would lead us to believe that the t procedures were not safe to use here? a. The sample medians and means for the two groups were slightly different. b. The distributions of the data were moderately skewed. c. The data are integers between 1 and 10 and so cannot be normal. d. Only the most severe departures from normality would lead us to believe the t procedures were not safe to use.

35. If we had used the more accurate software approximation to the degrees of freedom, we would have used which of the following for the number of degrees of freedom for the t procedures? a. 198 b. 191 c. 184 d. 99

Use the following to answer questions 36-37.

A newspaper conducted a statewide survey concerning a proposal to raise taxes in order to prevent budget cuts to education. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 580 would vote to raise taxes. Let p represent the proportion of registered voters in the state that would vote to raise taxes.

36. A 90% confidence interval for p is a. b. c. d.

37. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.5 as the value for p. a. n = 49. b. n = 1500. c. n = 4800. d. n = 9604.

Use the following to answer questions 38-40.

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion is less than 0.10, she will reject the shipment. To reach a decision she will test the hypotheses

using the large sample test for a population proportion. To do so, she selects an SRA of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects.

38. The P-value of her test is a. 0.4082. b. 0.0918. c. 0.0400. d. less than 0.0002.

39. Which of the following assumptions for inference about a proportion using a hypothesis test are violated? a. The data are an SRS from the population of interest. b. The population is at least 10 times as large as the sample. c. n is so large that both and are 10 or more, where is the proportion with major defects if the null hypothesis is true. d. There appear to be no violations.

40. A 95% plus four confidence interval for the true proportion of potatoes in the truck that have major defects is a. b. c. d.

Use the following to answer questions 41-42.

In a large Midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.

41. A 99% confidence interval for is a. b. c. d.

42. Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999? To determine this, you test the hypotheses

The P-value of your test is a. between .10 and .05. b. between .05 and .01. c. between .01 and .001 d. below .001.

43. A manufacturer receives parts from two suppliers. An SRS of 400 parts from supplier 1 finds 20 defective. An SRS of 100 parts from supplier 2 finds 10 defective. Let be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. A 95% confidence interval for is a. b. c. d.

Use the following to answer questions 44-45.

An SRS of 100 flights of a large airline (call this airline 1) showed that 64 were on time. An SRS of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let be the proportion of all flights that are on time for these two airlines.

44. A 95% confidence interval for the difference is a. b. c. d.

45. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses

The P-value of your test of the hypotheses given is a. between .10 and .05. b. between .05 and .01. c. between .01 and .001. d. below .001.

Labby rolled 12 dice 26,306 times. If each side is equally likely to come up, how many 1s, 2s, ..., 6s would he expect to have observed? 1/6 12/6 26,306 / 6 12 x 26,306 / 6

Which of the following methods is best way to calculate the p-value of the hypothesis test evaluating if Paul the Octopus' predictions are unusually higher than random guessing? Flip a coin 8 times, record the proportion of times where all 8 tosses were heads. Repeat this many times, and calculate the proportion of simulations where all 8 tosses were heads. Roll a die 8 times, record the proportion of times where all 8 rolls were 6s. Repeat this many times, and calculate the proportion of simulations where all 8 rolls were 6s. Flip a coin 10,000 times, record the proportion of heads. Repeat this many times, and calculate the proportion of simulations where more than 50% of tosses are heads.

Calculation Questions

Find the five number summary for the following age observations:

35, 45, 40, 20, 25, 41, 55, 62, 18, 22, 25, 40

Find the Standard Deviation of the following :

weight observation data:

100, 120, 130, 150, 140

Researchers randomly assigned 72 chronic users of cocaine into three groups: desipramine (antidepressant), lithium (standard treatment for cocaine) and placebo. Results of the study are summarized below.

What is the probability that a patient relapsed?

What is the probability that a patient received the antidepressant (desipramine) and relapsed?

If we know that a patient received the antidepressant (desipramine), what is the probability that they relapsed?

If we know that a patient relapsed, what is the probability that they received the antidepressant (desipramine)?

4- Write down the short-hand for a normal distribution with 2 (a) mean 5 and standard deviation 3,

(b) mean -100 and standard deviation 10, and

(c) mean 2 and standard deviation 9.

5- Auto insurance premiums. Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of $1,650. The article also states that 25% of California residents pay more than $1,800. (a) What is the Z-score that corresponds to the top 25% (or the 75th percentile) of the standard normal distribution?

(b) What is the mean insurance cost? What is the cutoff for the 75th percentile? (c) Identify the standard deviation of insurance premiums in California.

6-A random sample of 50 college students were asked how many exclusive relationships they have been in so far. This sample yielded a mean of 3.2 and a standard deviation of 1.74. Estimate the true average number of exclusive relationships using this sample.

Find pmales

Find pfemales

7- The third National Health and Nutrition Examination Survey collected body fat percentage (BF%) and gender data from 13,601 subjects ages 20 to 80. The average BF% for the 6,580 men in the sample was 23.9, and this value was 35.0 for the 7,021 women. The standard error for the difference between the average men and women BF%s was 0.114. Do these data provide convincing evidence that men and women have different average BF%s. You may assume that the distribution of the point estimate is nearly normal. Set hypotheses Calculate point estimate Check conditions Draw sampling distribution, shade p-value Calculate test statistics and p-value, make a decision

Which of the following does not need to be satisfied in order to conduct this hypothesis test using theoretical methods? Point price of one 0.99 Weights of diamonds are measured in carats 1 carat = 100 points, 0.99 carats = 99 points, etc. The difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the naked human eye, but does the price of a 1 carat diamond tend to be higher than the price of a 0.99 diamond? We are going to test to see if there is a difference between the average prices of 0.99 and 1 carat diamonds In order to be able to compare equivalent units, we divide the prices of 0.99 carat diamonds by 99 and 1 carat diamonds by 100, and compare the average point p

Which of the following is the correct set of hypotheses for testing if the average point price of 1 carat diamonds (pt100) is higher than the average point price of 0.99 carat diamonds (pt99)? H0 : pt99 = pt100 HA : pt99 pt100 H0 : pt99 = pt100 HA : pt99 > pt100 H0 : pt99 = pt100 HA : pt99 < pt100

carat diamond in the sample should be independent of another, and the point price of one 1 carat diamond should independent of another as well Point prices of 0.99 carat and 1 carat diamonds in the sample should be independent. Distributions of point prices of 0.99 and 1 carat diamonds should not be extremely skewed Both sample sizes should be at least 30

Which of the following does not need to be satisfied in order to conduct this hypothesis test using theoretical methods? Point price of one 0.99 carat diamond in the sample should be independent of another, and the point price of one 1 carat diamond should independent of another as well Point prices of 0.99 carat and 1 carat diamonds in the sample should be independent. Distributions of point prices of 0.99 and 1 carat diamonds should not be extremely skewed Both sample sizes should be at least 30

11- Use the following table to find the T statistic for inference on the difference of two means of 0.99 and 1 carats

12- Use the above table to find the degree of freedom (df)

13- An independent random sample is selected from an approximately oral population with unknown standard deviation. Find the degrees of freedom and the critical value (t*) for the given sample size and confidence level. a) n = 6, CL = 90%

b) n = 21, CL = 98%

c) n = 29, CL = 95%

d) n = 12, CL = 99%

14- Find the Correlation of the following two variables

X: 2, 3, 5, 6

Y: 1, 2, 4, 5