AP Statistics – Hoxmeier Tests about Population Mean Name: _______________________

1. An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Test the null hypothesis that the mean run time is 300 minutes against the alternative hypothesis that the mean run time is not 300 minutes. Use a 0.05 level of significance. (Assume that run times for the population of engines are normally distributed.)

2. A local chamber of commerce claims that the mean family income in a city is $12,250. An economist suspects otherwise and runs a hypothesis test using a sample of 135 families and finds a mean of $11,500 with a standard deviation of $3,180. Should the $12,250 claim be rejected at a 5% level?

3. The P-Value for a two sided test of the null hypothesis Ho :µ = 10 is 0.06 a) Does the 95% confidence interval for the mean include 10? Why or why not?

b) Does the 90% confidence interval for the mean include 10? Why or why not? 4. The P-Value for a two sided test of the null hypothesis Ho :µ = 15 is 0.03

a) Does the 99% confidence interval for the mean include 15? Why or why not?

b) Does the 95% confidence interval for the mean include 15? Why or why not? 5. A 95% confidence interval for µ is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0: µ = 0 versus

Ha: µ ≠ 0 at the α = 0.05 level, using the same data as used to construct the confidence interval. (a) We cannot test the hypothesis without the original data. (b) We cannot test the hypothesis at the α = 0.05 level since the α = 0.05 test is connected to the 97.5% confidence

interval. (c) We can make the connection between hypothesis tests and confidence intervals only if the sample sizes are large. (d) We would reject H0 at level α = 0.05. (e) We would accept H0 at level α = 0.05.

6. An appropriate 95% confidence interval for µ has been calculated as (−0.73, 1.92 ) based on n = 15 observations from

a population with a Normal distribution. The hypotheses of interest are H0: µ = 0 versus Ha: µ ≠ 0. Based on this confidence interval, (a) we should reject H0 at the α = 0.05 level of significance. (b) we should not reject H0 at the α = 0.05 level of significance. (c) we should reject H0 at the α = 0.10 level of significance. (d) we should not reject H0 at the α = 0.10 level of significance. (e) we cannot perform the required test since we do not know the value of the test statistic. 7. A certain population follows a Normal distribution with mean µ and standard deviation σ = 2.5. You collect data and test the hypotheses H0 : µ = 1, Ha : µ ≠ 1 You obtain a P-value of 0.022. Which of the following is true?

(a) A 95% confidence interval for µ will include the value 1. (b) A 95% confidence interval for µ will include the value 0. (c) A 99% confidence interval for µ will include the value 1. (d) A 99% confidence interval for µ will include the value 0. (e) None of these is necessarily true.

8.

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15. A union spokesman claims that 75% of union members will support a strike if their basic demands are not met. A company spokesman believes the true percentage is lower and runs a hypothesis test at the 10% significance level. What is the conclusion if 87 of 125 union members say they will strike?

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16. Some boxes of a certain brand of breakfast cereal include a voucher for a free video rental inside the box. The company that makes the cereal claims that a voucher can be found in 20 percent of the boxes. However, based on their experiences eating this cereal at home, a group of students believes that the proportion of boxes with vouchers is less than .2. This group of students purchased 65 boxes of the cereal to investigate the company’s claim. The students found a total of 11 vouchers for free video rentals in the 65 boxes.

Suppose it is reasonable to assume that the 65 boxes purchased by the students are a simple random sample of all boxes of this cereal. Based on this sample, is there support for the students’ belief that the proportion of boxes with vouchers is less than .2? Provide statistical evidence to support your answer.