Question

1. When testing gas pumps for accuracy, fuel-quality enforcement specialists test pumps and found that 1346 of them were not pumping accurately (within 3.3 ox when 5 gal is pumped), and 5612 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use a test for a population proportion.

2. In 1997, a survey of 820 households showed that 144 of them use email. Use those sample results to test the claim that more than 15% of households use email. Use a 0.05 significance level. Use a test for a population proportion.

3. In a recent poll of 745 randomly selected adults, 587 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 70% of adults say that it is morally wrong to not report all income on tax returns. Use a test for a population proportion.

4. Randomly selected statistics students participated in an experiment to test their ability to determine when 1 minute (or 60 seconds) has passed. Forty students yielded a sample mean of 56.3 seconds. Assuming that σ = 9.5 seconds, use a 0.05 significance level to test the claim that the population mean is equal to 60 seconds. Use a test for a population mean, with known standard deviation.

5. The health of the bear population in a national park is monitored by periodic measurements taken from anesthetized bears. A sample of 58 bears has a mean weight of 186.1 lbs. Assuming that σ is known to be 123.7 lb, use a 0.01 significance level to test the claim that the population mean of all such bear weights is greater than 155 lbs. Use a test for a population mean, with known standard deviation.

6. Last year, the average cost of making a movie was $54.8 million. This year, a sample of 15 recent action movies had an average production cost of $62.3 million with a sample standard deviation of $9.5 million. At the ? = 0.05 level of significance, can it be concluded that it costs more than average to produce an action movie? Use a test for a population mean, with σ unknown.

7. A national credit score company claims that the average credit score in the US is less than 679. A simple random sample of 12 credit rating scores is obtained. The mean credit score of the sample was 760.83 with a sample standard deviation of 58.15. Assuming the population is normally distributed, use a 0.05 significance level to test the company’s claim. Use a test for a population mean, with σ unknown.

8. A study found that the mean stopping distance of a school bus traveling 50 miles per hour was 264 feet. A group of automobile engineers decided to conduct a study of its school buses and found that for 20 buses, the mean stopping distance of the buses was 262.3 feet. The standard deviation of the population was 3 feet. Test the claim that the mean stopping distance of the company’s buses is actually less than 264 feet. Use a 0.01 significance level.

9. An article in a journal reports that 34% of American fathers take no responsibility for childcare. A researcher claims that the proportion is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with childcare. Test the researcher’s claim at a 0.05 significance level.

10. A light-bulb manufacturer advertises that the average life for its light bulb is more than 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours: 995 890 810 839 939 917 871 855 916 928 964 993 908 887 849 Do the data provide enough evidence to support the advertised claim? Use a 0.10 the significance level.

Answer 1

1. When testing gas pumps for accuracy, fuel-quality enforcement specialists test pumps and found that 1346 of them were not pumping accurately (within 3.3 ox when 5 gal is pumped), and 5612 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use a test for a population proportion.

Answer:

n = Total number of pumps = 1346 + 5612 = 6958

x = Number of inaccurate pumps = 1346

Claim: an industry representative that less than 20% of the pumps are inaccurate.

The null and alternative hypothesis is

H0: P = 0.20

H1: P < 0.20

Level of significance = 0.01

Test statistic is

P-value = P(Z < - 1.37) = 0.0859

P-value > 0.05 we fail to reject null hypothesis.

Conclusion:

An industry representative that NOT less than 20% of the pumps are inaccurate.

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