BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp

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1 BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time µ is changed by vigorous exercise, so you have a random sample of nine employees of your company (that you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x = 31.2 seconds to complete the maze. Use this information to test the hypotheses H0: µ = 30, Ha: µ 30 at the 1% significance level You conclude A) that H0 should be rejected. B) that H0 should not be rejected. C) that Ha should be accepted. D) this is a borderline case and no decision should be made. 2. An agricultural researcher plants 25 plots with a new variety of corn that is drought resistant and hence potentially more profitable. The average yield for these plots is x = 150 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean µ and that a 95% confidence interval for µ is found to be 150 ± Which of the following is true? A) A test of the hypotheses H0: µ = 150, Ha: µ 150 would be rejected at the 0.05 level. B) A test of the hypotheses H0: µ = 150, Ha: µ > 150 would be rejected at the 0.05 level. C) A test of the hypotheses H0: µ = 160, Ha: µ 160 would be rejected at the 0.05 level. D) All the above. 3. 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 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. Page 1

2 4. The mean area µ of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for µ are A) H0: µ = 1250 and Ha: µ B) H0: µ = 1250 and Ha: µ < C) H0: µ = 1250 and Ha: µ > D) not able to be specified without knowing the size of the sample used by the engineer. 5. In formulating hypotheses for a statistical test of significance, the null hypothesis is often A) a statement of no effect or no difference. B) the probability of observing the data you actually obtained. C) a statement that the data are all 0. D) Is the mean height for all adult American males between the ages of 18 and 21 now over 6 feet? If the population of all adult American males between the ages of 18 and 21 has mean height of µ feet and standard deviation σ feet, to answer this question one would test which of the following null and alternative hypotheses? A) H0: µ = 6 vs. Ha: µ > 6 B) H0: µ = 6 vs. Ha: µ < 6 C) H0: µ = 6 vs. Ha: µ 6 D) H0: µ = 6 vs. Ha: µ = 6 ± x, assuming our sample size is n. 7. In a statistical test of hypotheses, we say the data are statistically significant at level α if A) α = B) α is small. C) the P-value is less than α. D) the P-value is larger than α. Page 2

3 8. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) µ and standard deviation σ = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand give a mean of x = Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses H0: µ = 1.5, Ha: µ > 1.5 at the 5% significance level. You conclude A) that H0 should be rejected. B) that H0 should not be rejected. C) that Ha should be rejected. D) there is a 5% chance that the null hypothesis is true. 9. The level of calcium in the blood of healthy young adults follows a normal distribution with mean µ = 10 milligrams per deciliter and standard deviation σ = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is x = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this, test the hypotheses H0: µ = 10, Ha: µ < 10. The P-value of your test is A) less than B) C) D) greater than We test the null hypothesis H0: µ = 10 and the alternative Ha: µ < 10, for a normal population with σ = 4. A random sample of 16 observations is drawn from the 1 population and we find the sample mean of these observations is = 12. The P-value is 3 closest to A) B) C) D) Page 3

4 11. In the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican. A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed. Let p represent the proportion of the population of all adults over the age of 65 in the city who plan to vote Republican in the next presidential election. In terms of p, the researcher should test which of the following null and alternative hypotheses? A) H0: p = 0.47 vs. Ha: p > 0.47 B) H0: p = 0.47 vs. Ha: p 0.47 C) H0: p = 0.47 vs. Ha: p < 0.47 D) H0: p = 0.47 vs. Ha: p = 0.47 ± 0.03, because 0.03 is the margin of error for most polls. 12. Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time µ is changed by vigorous exercise, so you have a random sample of nine employees of your company (that you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. You compute the average time x that it takes these employees to complete the maze and test the hypotheses H0: µ = 30, Ha: µ 30. You find that the results are significant at the 5% level. You may also conclude A) the test would also be significant at the 10% level. B) the test would also be significant at the 1% level. C) both of the above. D) none of the above. Page 4

5 Answer Key 1. B 2. C 3. C 4. B 5. A 6. A 7. C 8. A 9. A 10. D 11. B 12. A Page 5

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