1. If, in a one-tail hypothesis test, the p-value equals=0.8121, what is the statistical decision if the null hypothesis is tested at the 0.02 level of significance? What is the statistical decision? 2. If SSR =120, why is it impossible for SST to equal 110? 3. In a random sample of 72 people, 18 are classified as "successful." a. Determine the sample proportion, p, of "successful" people. b. If the population proportion is 0.70, determine the standard error of the proportion. 4. A categorical variable has three categories, with the frequencies of occurrence below. a. Compute the percentage of values in each category. b. What conclusions can you reach concerning the categories? Category Frequency 10 A 10 29 B 29 11 C 11 5. The following is a set of data from a sample of n=6. 6 3 8 6 2 13 a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe the shape. 6. If P(A)=0.8, P(B)=0.6, and P(A and B)=0.48, are A and B independent? 7. A market researcher selects a simple random sample of n=100 users of a social media website from a population of over 100 million registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement. 8. If n=300 and X=120, construct a 95% confidence interval estimate of the population proportion. 9. If P(B)=0.1, P(A | B)=0.7, P(B)=0.9, and P(A | B)=0.6, find P(B | A). 10. Given a population of returns on endowment for private universities in one fiscal year, indicate what the sampling distribution for samples of 15 would consist of. 11. The following set of data is from a sample of n=7. 13 9 4 14 1 9 6 b. Compute the range, variance, standard deviation, and coefficient of variation. c. Compute the Z scores. Are there any outliers? d. Describe the shape of the data set. 12. Suppose you read a website that says that 32% of questions are answered by 10% of the students. On what type of data source is the claim in this story based? 13. If you want to be 99% confident of estimating the population mean to within a sampling error of 15 and the standard deviation is assumed to be 60, what sample size is required? 14. Which of the following events occur with a probability of zero? a. An animal that is a bird and cannot fly b. An organism that is both an animal and a plant c. A shape that is neither a circle nor a square d. A top that is spinning clockwise and counterclockwise 15. a. What is the probability that Z is less than 1.05? b. What is the probability that Z is greater than 0.29? c. What is the probability that Z is less than 0.29 or greater than the mean? d. What is the probability that Z is less than 0.29 or greater than 1.05? 16. Yi=190.8Xi a. Interpret the meaning of the Y-intercept, b0. b. Interpret the meaning of the slope, b1. c. Predict the mean value of Y for X=4. 17. Consider a population of 1024 mutual funds that primarily invest in large companies. You have determined that , the mean one-year total percentage return achieved by all the funds, is 9.30 and that , the standard deviation, is 3.00. a. According to the empirical rule, what percentage of these funds is expected to be within 2 standard deviations of the mean? b. According to the Chebyshev rule, what percentage of these funds are expected to be within 4 standard deviations of the mean? c. According to the Chebyshev rule, at least 88.89% of these funds are expected to have one-year total returns between what two amounts? 18. Form an ordered array, given the following data from a sample of n = 7 midterm exam scores in accounting. 65 73 71 77 67 99 94 19. For a sample of size n, the cumulative area for the ith smallest value corresponds to a cumulative area of i / n+1. . For a sample of n=19, list the Z values that correspond to the 6 smallest values. 20. A lock on a bank vault consists of three dials, each with 1010 positions. In order for the vault to open, each of the three dials must be in the correct position. a. How many different possible dial combinations are there for this lock? b. What is the probability that if you randomly select a position on each dial, you will be able to open the bank vault? c. Explain why "dial combinations" are not mathematical combinations expressed by the nCx=n! / x!(nx)!. 21. If, in a sample of n=25 selected from a normal population, X=57 and S=15, how many degrees of freedom does the t test have if you are testing the null hypothesis H0: =50? 22. You want to select a random sample of n=1 from a population of three items (which are called A, B, and C). The rule for selecting the sample is as follows: Flip a coin; if it is heads, pick item A; if it is tails, flip the coin again; this time, if it is heads, choose B; if it is tails, choose C. Explain why this is a probability sample but not a simple random sample. 23. If, in a (two-tail) hypothesis test, the p-value is 0.1367, what is your statistical decision if you test the null hypothesis at the 0.08 level of significance? 24. Determine the upper-tail critical value t Subscript alpha divided by 2 t/2 in each of the following circumstances. a 1=0.95, n=30 . b 1=0.99, n=30 d e 1=0.95, n=41 1=0.90, n=61 c 1=0.95, n=22 25. If, in a random sample of 200 items, 32 are defective, what is the sample proportion of defective items