Math227S Practice Exam #4

发布时间：2025-05-14

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Math227S Practice Exam #4 Ch. 8, 9

1. Express the original claim, the null hypothesis, and the alternative hypothesis in symbolic form.

a. A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness.

b. A scientist claims that the mean body temperature is less than or equal to 98.6 ℉ .

c. An entomologist writes an article in a scientific journal which claims 16 in one thousand male fire flies are unable to produce light due to a genetic mutation.

2. Suppose we want to test the claim that less than 40% of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

3. In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won. Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate.

4. A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent winners are from a population with a mean BMI less than 20.16, which was the BMI for winners from the 1920s and 1930s.

19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8

5. The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.2 minutes or less. A random sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.8 minutes. Use a 0.01 significance level to test the claim that the standard deviation is less than or equal to 1.2 minutes.

6. A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60. A random sample of major brands of syrup is selected, and the number of calories is shown. Test the claim using a significance level 0.10.

53 210 100 200 100 220 210 100 240 200 100 210 100 210 100 60 100 210

7. The number of grams of carbohydrates contained in 1-ounce servings of randomly selected

chocolate and nonchocolate candy is shown. Is there sufficient evidence to conclude that there is a difference between the variation in carbohydrate content for chocolate and nonchocolate candy? Use a significance level 0.10.

Chocolate	29	25	17	36	41	25	32	29	38	34	24	27	29
Nonchocolate	41	41	37	29	30	38	39	10	29	55	29

8. A random sample of nine local banks shows their deposits (in billions of dollars) 3 years ago and their deposits (in bollions of dollars) today. Using a significance level 0.05, can it be concluded that the average in deposits for the banks is greater today than it was 3 years ago? Assume the variable is normally distributed.

3 years ago	11.42	8.41	3.98	7.37	2.28	1.10	1.00	0.9	1.35
Today	16.69	9.44	6.53	5.58	2.92	1.88	1.78	1.5	1.22

9. A recent random survey of households found that 14 out of 50 householders had a cat and 21 out of 60 householders had a dog. Use a 0.05 significance level to test the claim that fewer household owners have cats than household owners who have dogs as pets.

10. A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a random sample of 26 elementary school teachers is $48,256, and the sample standard deviation is $3,912.40. The mean of the salaries of a random sample of 24 secondary school teachers is $45,633. The sample standard deviation is $5533. Using a significance level 0.05, can it be concluded that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers?