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# General Statistics

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1. Z-test
A researcher wishes to test the claim that the average age of lifeguards in Ocean City is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7 years with a standard deviation of 2 years. Is there evidence to support her claim at a 95% level of confidence?

2. T-test for Unpaired data
Consider the following situation describing layoffs at a manufacturing plant of the Monsanto Company. Does there appear to be a case of age discrimination between those laid off and those non-laid off?

Employee age layoff status
1 51 no
2 58 no
3 48 no
4 53 yes
5 45 yes
6 43 yes
7 49 no
8 59 no
9 56 yes
10 56 yes
11 54 no
12 55 yes
13 54 no
14 48 no
15 39 no
16 47 no
17 59 yes
18 58 no
19 55 yes
20 57 yes
21 57 yes
22 53 no

(Gregory L. Harper, "Statistics as evidence of age discrimination," The hastings law journal, vol 32, may 1981, pp. 1347-1375)

3. Z-test
A physician claims that joggers maximal volume oxygen uptake is greater than the average of all adults. A sample of 15 joggers has a mean of 40.6 milliliters per kilogram and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician's claim at 95%?

Explain the difference between testing a single mean and testing the difference between two means

5. Chi-square
The advisor of an ecology club at a large college expects that the group consists of 10% freshman, 20% Sophomores, 40% Juniors and 30% Seniors. The membership for the club this year is observed to be 14 freshman, 19 sophomores, 51 Juniors and 16 Seniors. At 95% level of confidence, test the advisors belief.