QUESTION 2

1. A stock investor would like to have an idea concerning the average return of stocks that are traded on a certain exchange. In a sample of 96 stocks, the average return was 11 percent with a standard deviation of 12 percent. What is theupper boundof the 99% confidence interval? (please express your answer as a PERCENT using 2 decimal places)

5 points

QUESTION 3

1. Suppose the country club bills based on a sample of 4 members are: 434, 1,021, 650, 890. What is the standard deviation for this sample of bills? (please round your answer to 1 decimal place)

15 points

QUESTION 4

1. In a survey of 161 publicly-traded companies, the average price-earnings ratio was 18.2 with a standard deviation of 8. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past value of 16.8, what is the critical value? (please round your answer to 2 decimal places)

5 points

QUESTION 5

1. In the past, the value of houses a local realtor has sold is normally distributed with a mean of $185,000 with a standard deviation of $30,000. What is the probability that the next house the realtor sells has a value over $150,000? (please round your answer to 4 decimal places)

10 points

QUESTION 6

1. Suppose that an individual stock?s return is normally distributed with a mean of 10% and a standard deviation of 8%. Suppose that all stocks had the same distribution of returns. Suppose that all stocks have the same distribution of returns (and the return on 1 stock is independent of the return on another stock). What is the probability that in a sample of 40 stocks that the average return is at least 12%? (please round your answer to 4 decimal places)

10 points

QUESTION 7

1. Suppose the number of different accounts the family members have at a bank is given by the following probability distribution: 50% of the families have 1 account; 25% of the families have 2 accounts; 13% of the familiies have 3 accounts, and the remaining families have 4 accounts. What is the expected number of accounts of a randomly chosen family? (please round your answer to 2 decimal places)

15 points

QUESTION 8

1. Suppose that you have bought a total of 3200 shares of stock of a particular company. You bought 1300 shares of stock at $17 per share, 800 shares of stock at $10 per share, and the remaining shares at $20 per share. What is the average price you paid per share of stock? (please round your answer to 2 decimal places)

15 points

QUESTION 9

1. Suppose that a particular large hotel has 790 rooms. Furthermore, suppose that the demand for the hotel's rooms are normally distributed with a mean demand of 725 rooms with a standard deviation of 39 rooms. How many rooms must the hotel sell if this coming weekend is to be in the bottom 20% of the slowest weekends? (please round your answer to 2 decimal places)

10 points

QUESTION 10

1. In an effort to reduce energy costs, a major university has installed more efficient lights as well as automatic sensors that turn the lights off when no movement is present in a room. Historically, the cost of lighting an average classroom for 1 week has been $265. To determine whether the changes have signficantly reduced costs, the university takes a sample of 84 classrooms. They find that the average cost for 1 week is $244 with a standard deviation of $63. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past, what is the test statistic? (please round your answer to 2 decimal places)

5 points

QUESTION 11

1. What is the t-value associated with 25 degrees of freedom and 20% in the tail? (please round your answer to 3 decimal places)

10 points

QUESTION 12

1. A sample of 60 mutual funds was taken and the mean return in the sample was 13% with a standard deviation of 6.9%. The return on a particular index of stocks (against which the mutual funds are compared) was 11.5%. Therefore, the test statistic is 1.68. When testing the hypothesis that the average return on actively-managed mutual funds is higher than the return on an index of stocks, if the critical value is 1.96, what is your conclusion concerning the null hypothesis?

   Reject the null hypothesis

   Fail to reject the null hypothesis

5 points

QUESTION 13

1. Suppose the following data show the prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 6.1, 11.3, 9.5, 10.5. Calculate the mean selling price of the sample. (please express your answer using 2 decimal places)

15 points

QUESTION 14

1. To determine whether high blood pressure affected whether a person had a stroke, a sample of 150 people who had had strokes are examined. In the sample, 37% had high blood pressure. If we were to test the hypothesis that at least 33% of the people who have had strokes have had high blood pressure (using the 5% level of signficance), what is the p-value? (please round your answer to 4 decimal places)

1) Numerical Summary Statistics a) Sample size (n) b) Population size (N) c) arithmetic mean i) sample mean ( X ) n x i i =1 n ii) population mean () N x i i =1 N d) weighted mean n x w i i i =1 n Xw = w i i =1 e) Range i) maximum observation - minimum observation f) Variance i) sample variance (s2) n (x X) 2 i i =1 n 1 g) Standard deviation i) sample standard deviation (s) s2 h) Mean Absolute Deviation n x X i i =1 n i) Covariance n [(x i X )( y i Y )] i =1 n 1 j) Correlation cov ariance x y k) Standardized value of x Z= x x x where x is the mean of x and x is the standard deviation of x l) Coefficient of Variation s tan dard deviation CV = 100 * mean 2) Discrete Probability Distributions a) Expected value of a random variable n E( X ) = X = xi P( X = xi ) i =1 b) variance of a random variable n 2 V ( X ) = X = [xi E( X )] P( X = xi ) 2 i =1 c) Standard deviation of a random variable V( X ) 3) Continuous Distributions a) Standardized score x x x 4) Sampling Distributions a) Mean of the sample mean, X E( X ) = X = b) Standard deviation of the sample mean s X = n X = s n X c) Mean of the sample proportion, p E( p ) = p = p d) Standard deviation of the sample proportion p( 1 p ) p = n p = p p(1 p ) n p 5) Confidence Interval X Z X or X t df , X (where d.f. if the degrees of freedom) 2 2 p Z p 2 where X = s n and p = p( 1 p ) n 6) Hypothesis Testing a) Test statistic for the sample mean X 0 s n (1) where 0 is the hypothesized mean (2) This test statistic has a Z distribution if n > 30 and a t-distribution (with n1 degrees of freedom) if n =12). The relevant z-score here is based on the z-score formula Meaning, P(x>=12) is equivalent to the case that z= X 1210 = 1.58 . / n 8/ 40 P( z 1.58) . Now, it either has to be the case that z 1.58 or z=12). The relevant z-score here is based on the z-score formula Meaning, P(x>=12) is equivalent to the case that z= X 1210 = 1.58 . / n 8/ 40 P( z 1.58) . Now, it either has to be the case that z 1.58 or z