Survey analysis questions: interpreting opinion polls, training manager at a manufacturing firm and the San Francisco Department of Public Health

1.
You are interpreting the results of an opinion poll. In a random sample of 100 small business owners, you find that of the 40 large business owners, a total of 30 support a proposal to implement a local sales tax. Of the 60 small business owners, 20 support it. How can you determine if there is a relationship between size of business owned and whether the owner is likely to support a sales tax?

2.
You are a training manager for a manufacturing firm and have three new training programs to assess. You assign, at random, equal numbers of employees to each of the training programs in order to determine which program is most efficient. How might you go about analyzing the results?

3.
Here’s a link to a report by the San Francisco Department of Public Health that suggests criminals are more likely to own a gun than non-criminals: http://www.dph.sf.ca.us/Reports/Firearms/Part7Criminal.pdf What does this suggest to you?

4.
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is:

Number of months before first raise in salary

CPA Inc. AB Int. Acct. Ltd. Pfisters

12 14 18 12

10 12 12 14

14 10 16 16

12 10

At the .05 level of significance, is there a difference in the mean number of months before a raise was granted among the four firms?
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Answer 1. If I am interpreting the results of an opinion poll, then if a random sample of 100 small businesses is taken and I find that out of 40 large businesses, 30 support a proposal to implement a local sales tax. Then I find that the probability of a large business owner supporting a proposal to implement a sales tax is likely to be 30/40 that is 0.75. And the probability of a small business owner supporting a sales tax is likely to be 20/60 that is 0.33. So we can say that there is a relationship between the size of the business and the probability that the owner is going to support the proposal for a local sales tax.

Answer 2. If I am a training manager and I want to measure the efficiency of each of the three training …