If you choose to solve these problems, please show the steps and formulas used.
1. A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. At = .05, what is the value the test statistic?
Sample size 50 80
Mean effect 7 6.95
Sample variance 3 4
A. t = 3.252
B. z = 0.455
C. z = 0.081
D. z = 0.151
2. A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the .10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
Pine trees Spruce trees
Sample size 40 70
Mean trunk diameter (cm) 45 39
Sample variance 100 150
A. The data does not support the claim because the test value 1.29 is greater than 1.28.
B. The data supports the claim because the test value 2.78 is greater than 1.28.
C. The data supports the claim because the test value 2.78 is greater than 1.64.
D. The data does not support the claim because the test value 1.29 is less than 1.64.
3. A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the variation of the amount of money spent on lunches. The variance of nine business dinners was $6.12 and the variance of 12 business lunches was $0.87. What is the test value?
The solution provides answers to multiple choice questions on hypothesis testing. Relevant workings and formula for the calculation are also included. Please refer to the attached Word document for the formatted solution.