Math 221 Quiz Answers
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Math 221 Quiz Answers

Course: MATH 221, Spring 2007

School: DeVry Houston

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PRACTICE QUIZ ANSWERS MC 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem: A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean. Points: (712.0, 768.0) (636.9, 653.1) CORRECT ANSWER (539.6, 551.2) (112.0, 118.9) MC 2....

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QUIZ PRACTICE ANSWERS MC 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem: A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean. Points: (712.0, 768.0) (636.9, 653.1) CORRECT ANSWER (539.6, 551.2) (112.0, 118.9) MC 2. MULTIPLE CHOICE In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean. Points: (18.3, 20.9) (19.1, 20.4) (17.5, 21.7) CORRECT ANSWER (14.1, 23.2) SA 3. SHORT ANSWER. The Marketing analyst of a major e-commerce site claims that the mean time for someone to checkout an item is at most 5 minutes. Write the null and alternative hypotheses. Points: MC 4. MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question: The mean age of bus drivers in Chicago is greater than 51.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? Points: There is sufficient evidence to reject the claim mu > 51.3. There is sufficient evidence to support the claim mu > 51.3. CORRECT ANSWER There is not sufficient evidence to reject the claim mu > 51.3. There is not sufficient evidence to support the claim mu > 51.3. SA 5. A fast food outlet claims that the mean waiting time in line is less than 3.9 minutes. A random sample of 60 customers has a mean of 3.8 minutes with a standard deviation of 0.6 minute. If alpha = 0.05, test the fast food outlet's claim using P-values. Points: Instructor Explanation : P-value = 0.0985, P > alpha, fail to reject; There is not sufficient evidence to support the claim that the mean waiting time is less than 3.9 minutes. EQ 6. Which is wider -- a 99% confidence interval or a 90% confidence interval? Explain why this is so. Points: Instructor Explanation : the 99% is wider because to claim that amount of certainty one must include more possibilities it is mathematically because so of the z-score which corresponds to the 2 areas under the curve. The absolute value of a z-score corresponding to 99% is bigger than the absolute value of a z-score corresponding to 90%. Because this number is used in the numerator of the formula for E, we add a bigger number in here: (mu - E, mu + E) giving the wider interval. EQ 7. The mean score for all NBA games during a particular season was less than 93 points per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis. Points: Instructor Explanation : The claim is that the mean is less that 93. Since it doesn't include the equal sign it is the alternative hypothesis. Thus, the null is Ho: mu >= 93. A decision that fails to reject the null says that there is not enough evidence to support the claim of mu < 93. EQ 8. What z-scores would be used to create an 89% confidence interval? Points: Instructor Explanation : An 89% confidence interval has an area of .8900 between the zscores which means that .1100 is in the tails. Since the curve is symmetric, .11002 is in each tail which is .0550. Using the table we find the z-score corresponding to .055 to be 1.60. Also because the curve is symmetric the z-score +1.60 applies. EQ 9. A soccer ball manufacturer wants to estimate the mean circumference of minisoccer balls within .12 inch. Assume that the population of circumferences is normally distributed. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population's standard deviation is .2 inches. Points: Instructor Explanation : The formula to determine n is n = (z-sub c times sigma divided by E) In this case the acceptable error is .12. So we have (1.96 times .2 divided by .12) = 10.67111... which rounds UP to 11 and we ALWAYS round up when determining sample size. We need a sample of 11. EQ 10. The local union claims that the mean age of bus drivers is 50.1 years. If a hypothesis test is performed, will it be left tailed, right tailed, or two-tailed? Points: Instructor Explanation : Since the null is mu = 50.1, it will be two tailed.

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