QUESTION 1

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, 1000 shares of stock at $12 per share, and the remaining shares at $21 per share. What is the average price you paid per share of stock? (please round your answer to 2 decimal places)

15 points

QUESTION 2

1. Suppose that an individual stock?s return is normally distributed with a mean of 10% and a standard deviation of 8%. What is the probability that the stock?s return will be at least 16%? (please round your answer to 4 decimal places)

10 points

QUESTION 3

1. In a survey of 120 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis (at the [a]% level of significance) that the average energy use has decreased from the past value of 16.8, the p-value is 0.0116. Therefore, if you are using a 10% level of significance that the average price-earnings ratio has decreased from the past, what is your conclusion concerning the null hypothesis?

   Reject the null hypothesis

   Fail to reject the null hypothesis

5 points

QUESTION 4

1. Suppose that the number of guests per month that members of a country club bring to golf is given by the following probability distribution: 57% of the members don't have any guests each month, 17% of the members have 1 guest per month to the club; 14% of the members have 2 guests per month; and the remaining members have 3 guests per month. What is the expected value of the number of guests that members bring out each month? (please express your answer using 2 decimal places)

15 points

QUESTION 5

1. In a sample of 84 grocery store customers, it is found that 66% of them were buying 15 items or fewer. Determine theupper boundof the 95% confidence interval for the proportion of customers that buy 15 items or fewer? (please express your answer AS A DECIMAL using 4 decimal places)

5 points

QUESTION 6

1. Suppose that the probability that any stock increases in price (over a 3 month period of time) is 60%. What is the probability that in a sample of 145 stocks that you buy that less than 55% increase in price (over a 3 month period of time)? (please round your answer to 4 decimal places)

10 points

QUESTION 7

1. Suppose the profit the Honda dealership makes on the next 5 Accords it sells are: 388, 952, 674, 553, 1,368. What is the average profit on these cars?

15 points

QUESTION 8

1. Suppose the following data show the prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 5.6, 5.6, 13.2, 6.9. Calculate the standard deviation of the sample of selling prices. (please express your answer using 2 decimal places)

15 points

QUESTION 9

1. Suppose that historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine whether the proportion of new car buyers that trade in their old car has statistically significantly decreased,what is the p-value? (please round your answer to 4 decimal places)

5 points

QUESTION 10

1. A sample of 51 mutual funds was taken and the mean return in the sample was 13.9% with a standard deviation of 9.2%. The return on a particular index of stocks (against which the mutual funds are compared) was 11.8%. When testing the hypothesis (at the 5% level of significance) that the return on actively-managed mutual funds is higher than an index of stocks, 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 16 degrees of freedom and 1% in the tail? (please round your answer to 3 decimal places)

10 points

QUESTION 12

1. Nationwide, the mean amount of sales each week at Lowe?s store is normally distributed with a mean of $6 million with a standard deviation of $0.86 million. Lowe?s has decided to close 15% of its stores, and has chosen amount of sales as the criterion on which the decision will be based (they are going to close the 15% of the stores with the lowest sales). How much in sales does a store have to have in order tonotbe closed? (please express your answer in millions and round your answer to 2 decimal places)

10 points

QUESTION 13

1. An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 99 clients of an online stock trading company, the average number of trades per year was 87 with a standard deviation of 15. If you were to test the hypothesis that the average number of trades per year is greater than than the previous year when the average number of trades was 85 (using the 10% level of significance), what is the critical value? (please round your answer to 2 decimal places)

5 points

QUESTION 14

1. An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 120 clients of an online stock trading company, the average number of trades per year was 82 with a standard deviation of 16. If you were to test the hypothesis that the average number of trades per year is different than the previous year when the average number of trades was 85 (using the 10% level of significance), what is the null and alternative hypotheses?

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