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1. Are stock splits beneficial to stockholders? SNL Financial studied stock splits in the banking industry over an 18-month period. For a sample of 20 stock splits, 15 led to an increase in investment value, 3 led to a decrease in investment value, and 2 resulted in no change. Conduct a sign test to determine if it can be concluded that stock splits are beneficial for holders of bank stocks.
a) What are the null and alternative hypotheses?
b) Using α = .01, what is your conclusion?
2. A poll taken during the recession in 2008 asked 600 adults a series of questions about the state of the economy and their children’s future. One question was, “Do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours?” The responses showed 240 better, 310 worse, and 50 about the same. Use the sign test and α = .01 to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. What is your conclusion?
3. A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the median delivery times for the two services? Use a .10 level of significance for the test.
Service Delivery 1 2
1 24.5 28.0
2 26.0 25.5
3 28.0 32.0
4 21.0 20.0
5 18.0 19.5
6 36.0 28.0
Service Delivery 1 2
7 25.0 29.0
8 21.0 22.0
9 24.0 23.5
10 26.0 29.5
11 31.0 30.0
4. Unisys maintains a hurricane database which provides information on hurricanes in the Atlantic/Caribbean/Gulf of Mexico and the Eastern Pacific Ocean. Maximum wind speeds in knots for a sample of hurricanes over the past four hurricane seasons are shown. Use α = .10 and test to determine whether the distribution of hurricane wind speeds is the same for these two regions. What is your conclusion?
Atlantic/Carribean/Gulf of Mexico Eastern Pacific Ocean
Storm Max Wind Speed Storm Max Wind Speed
Frances 125 Darby 105
Jeanne 110 Frank 75
Lisa 65 Isis 65
Emily 135 Hilary 90
Ophelia 80 Max 70
Rita 150 Bud 110
Wilma 150 Daniel 130
Ernesto 65 Sergio 95
Florence 80 Cosme 65
Helene 105 Flossie 120
Dean 145 Henriette 75
Karen 60 Ivo 70
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