CHAPTER 6 REVIEW QUIZ (11 POINTS)

1. / A researcher is interested in the size of the current balance of credit card holders. To estimate this, he obtains the size of the current balance of a random sample of 25 credit card holders. A 90% confidence interval for the mean current balance of credit card holders is found to be $662.72 ± $44.70. Which of the following would produce a confidence interval with a smaller margin of error than this 90% confidence interval?
A) / Obtain the balances of only five credit card holders rather than 25, because five are likely to be more uniform than 25.
B) / Obtain the balances of 100 credit card holders rather than 25.
C) / Compute a 99% confidence interval rather than a 90% confidence interval. The increase in confidence indicates that we have a better interval.
D) / None of the above.

Ans: B

2. / You measure the weights of a random sample of 400 male workers in the automotive industry. The sample mean is = 176.2 lbs. Suppose that the weights of male workers in the automotive industry follow a normal distribution with unknown mean  and standard deviation  = 11.1 lbs. A 95% confidence interval for  is
A) / (154.44, 197.96).
B) / (157.94, 194.46).
C) / (175.11, 177.29).
D) / (175.29, 177.11).

Ans: C

3. / Twenty-five credit card holders are selected at random. For each, their current credit card balance is recorded. The average for these 25 people is = $600. Assume that the current balance of all credit card holders follows a normal distribution with unknown mean  and that a 90% confidence interval for  is found to be $600 ± $32.90. What can we deduce about the standard deviation  of current credit card balances?
A) /  is about $100.
B) /  will be larger than if we used 100 credit card holders.
C) /  is $32.90.
D) / If we repeatedly took samples of 25 credit card holders many, many additional times and from each sample computed a 90% confidence interval, in approximately 90% of these  would be within $32.90 of the mean.

Ans: A

4. / In a large city, the percent of total spending that households devote to housing is normally distributed, with mean  and standard deviation  = 9%. I select a simple random sample of four young households and determine the percent of their total spending that is devoted to housing. The four percentages are
33% / 39% / 32% / 36%.
Based on these data, a 99% confidence interval for  is
A) / 35% ± 5.78%.
B) / 35% ± 8.82%.
C) / 35% ± 11.59%.
D) / 35% ± 23.18%.

Ans: C

5. / In tests of significance about an unknown parameter, the test statistic
A) / is the value of the unknown parameter under the null hypothesis.
B) / is the value of the unknown parameter under the alternative hypothesis.
C) / measures the compatibility between the null and alternative hypotheses.
D) / measures the compatibility between the null hypothesis and the data.

Ans: D

6. / 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.

Ans: B

7. / In a statistical test of hypotheses, we say the data are statistically significant at level  if
A) /  = 0.05.
B) /  is small.
C) / the P-value is less than .
D) / the P-value is larger than .

Ans: C

8. / The level of calcium in the blood of healthy young adults follows a normal distribution with mean  = 10 milligrams per deciliter and standard deviation  = 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 = 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:  = 10, Ha:  < 10.
The P-value of your test is
A) / less than 0.0002.
B) / 0.3085.
C) / 0.6170.
D) / greater than 0.99.

Ans: A

9. / A researcher wishes to determine if listening to classical music improves the concentration of office workers. To investigate this, he decides to see if office workers are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose the time (in seconds) needed for office workers to complete the maze while listening to classical music follows a normal distribution with mean  and standard deviation  = 4. Suppose also, that in the general population, the time needed to complete the maze (without listening to classical music) follows a normal distribution with mean 40 and standard deviation  = 4. The researcher, therefore, decides to test the hypotheses
H0:  = 40, Ha:  < 40.
To do so, the researcher has 10,000 office workers complete the maze with classical music playing. The mean time for these workers is = 39.8 seconds and the P-value is less than 0.0001.
Suppose that two office workers decide to see if they get the same results as the researcher. They both take the maze while listening to classical music. The mean of their times is = 39.8 seconds, the same as that of the researcher. It is appropriate to conclude which of the following?
A) / They have reproduced the results of the researcher and their P-value will be the same as that of the researcher.
B) / They have reproduced the results of the researcher, but their P-value will be slightly smaller than that of the researcher.
C) / They will reach the same statistical conclusion as the researcher, but their P-value will be a bit different than that of the researcher.
D) / None of the above.

Ans: D

10. / A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The explanation is
A) / the placebo effect is present which limits statistical significance.
B) / the sample size is too small to determine if the observed increase cannot be reasonably attributed to chance.
C) / that although the survival time has doubled, in reality the actual increase is really two years.
D) / the calculation was in error. The researchers forgot to include the sample size.

Ans: B

11. / Does taking ginkgo tablets twice a day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects who took ginkgo tablets twice a day for a period of six months. At the end of the study, 200 variables related to the mental performance of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Nine of these variables were significantly better (in the sense of statistical significance) at the 5% level for the group taking the ginkgo tablets as compared to the population as a whole, and one variable was significantly better at the 1% level for the group taking the ginkgo tablets as compared to the population as a whole. It would be correct to conclude
A) / there is good statistical evidence that taking ginkgo tablets twice a day provides some improvement in mental performance.
B) / there is good statistical evidence that taking ginkgo tablets twice a day provides improvement for the variable that was significant at the 1% level. We should be somewhat cautious about making claims for the variables that were significant at the 5% level.
C) / these results would have provided good statistical evidence that taking ginkgo tablets twice a day provides some improvement in mental performance if the number of subjects had been larger. It is premature to draw statistical conclusions from studies in which the number of subjects is less than the number of variables measured.
D) / none of the above.

Ans: D