Question

We have learned hypothesis tests

1. for the mean (when population variance is known and when it is unknown)
2. for a percentage
3. to see if the means of two sets of data are the same
4. goodness of fit test
5. test for independence

For each type give a brief example. You do not have to solve the problem you give.

Answer 1

1. example of hypothesis testing for the mean when population variance is known

Boys of a certain age are known to have a mean weight of μ = 85 pounds. A complaint is made that the boys living in a municipal children's home are underfed. As one bit of evidence, n = 25 boys (of the same age) are weighed and found to have a mean weight of ¯xx¯ = 80.94 pounds. It is known that the population standard deviation σ is 11.6 pounds (the unrealistic part of this example!). Based on the available data, what should be concluded concerning the complaint?

2. example of hypothesis testing for the mean when population variance is unknown :

It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population?

3. example of hypothesis testing for a percentage

The CEO of a large electric utility claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisified. Based on these findings, can we reject the CEO's hypothesis that 80% of the customers are very satisfied?

4. example of hypothesis testing to see if the means of two sets of data are the same

The Acme Company has developed a new battery. The engineer in charge claims that the new battery will operate continuously for at least 7 minutes longer than the old battery.

To test the claim, the company selects a simple random sample of 100 new batteries and 100 old batteries. The old batteries run continuously for 190 minutes with a standard deviation of 20 minutes; the new batteries, 200 minutes with a standard deviation of 40 minutes.

Test the engineer's claim that the new batteries run at least 7 minutes longer than the old.

5. example of hypothesis testing for goodness of fit test

Acme Toy Company prints baseball cards. The company claims that 30% of the cards are rookies, 60% veterans but not All-Stars, and 10% are veteran All-Stars.

Suppose a random sample of 100 cards has 50 rookies, 45 veterans, and 5 All-Stars. Is this consistent with Acme's claim?

6. example of hypothesis testing for test for independence

public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Republican, Democrat, or Independent) Do the men's voting preferences differ significantly from the women's preferences?