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AP Statistics - Chapter 6 Warm-Ups
1. A 95% confidence interval for the mean  of a population is computed from a random sample and found to be
9  3. We may conclude
A) that there is a 95% probability that  is between 6 and 12
B) that there is a 95% probability that the true mean is 9 and there is a 95% chance that the true margin of error is 3
C) that if we took many, many additional random samples and from each computed a 95% confidence interval for ,
approximately 95% of these intervals would contain .
D) all of the above
2. The records of all 100 postal employees at a postal station in a large city showed that the average amount of time
these employees had worked for the U.S. Postal Service was J = 8 years. Assume that we know that the standard
deviation of the amount of time U.S. Postal Service employees have spent with the Postal Service is approximately
normal with standard deviation  = 5 years. A 95% confidence interval for the mean time  the population of U.S.
Postal Service employees has spent with the postal service based on these data is
A) 8 ± 0.82
B) 8 ± 0.98
C) 8 ± 9.80
D) not trustworthy
6. An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average
yield for these plots is found to be 162.72  4.47 bushels per acre. Which of the following would produce a
confidence interval with a smaller margin of error than this 90% confidence interval?
A) planting only five plots rather than 25, since five are easier to manage and control
B) planting 100 plots rather than 25
C) computing 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
You measure the heights of a random sample of 400 high school sophomore males in a Midwestern state. The sample mean is
J = 66.2 inches. Suppose that the heights of all high school sophomore males follow a normal distribution with unknown
mean  and standard deviation  = 4.1 inches.
7. A 95% confidence interval for  is
A) (58.16, 74.24)
B) (59.46, 72.94)
C) (65.8, 66.6)
D) (65.86, 66.54)
8. I compute a 95% confidence interval for . Suppose I had measured the heights of a random sample of 100
sophomore males rather than 400. Which of the following statements is true?
A) The margin of error for our 95% confidence interval would increase
B) The margin of error for our 95% confidence interval would decrease
C) The margin of error for our 95% confidence interval would stay the same, since the level of confidence has not
changed
D)  would decrease
10. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is J = 150
bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with
unknown mean  and that a 90% confidence interval for  is found to be 150  3.29. What can we deduce about
the standard deviation  of the yield per acre for the new variety of corn?
A)  is about 10
B)  will be larger than if we used 100 plots
C)  is 3.29
D) If we repeated the experiment many, many additional times and from each computed a 90% confidence interval, in
approximately 90% of these  would be within 3.29 of the mean
11. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly
weighed a total of n times and the mean J of the weighings is computed. Suppose the scale readings are normally
distributed with unknown mean  and standard deviation  = 0.01 grams. How large should n be so that a 95%
confidence interval for  has a margin of error of  0.0001?
A) 100
B) 196
C) 10,000
D) 38,416
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16. Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year
at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal
distribution with a standard deviation  = $30. The number of observations required is closest to
A) 25
B) 30
C) 609
D) 865
17. Other things being equal, the margin of error of a confidence interval increases as
A) the sample size increases B) the confidence level decreases C) the population st.dev increases D) none of these
18. Researchers are studying yield of a crop in two locations. The researchers are going to compute independent 90%
confidence intervals for the mean yield at each location. The probability that at least one of the intervals will cover
the true mean yields at their location is
A) 0.81
B) 0.19
C) 0.99
D) 0.95
23. 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, Ha: p > 0.47
B) H0: p = 0.47, Ha: p  0.47
C) H0: p = 0.47, Ha: p < 0.47
D) H0: p = 0.47, Ha: p = 0.47  0.03, since 0.03 is the margin of error for most polls.
24. The mean area  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 
A) are H0:  = 1250, Ha:   1250
B) are H0:  = 1250, Ha:  < 1250
C) are H0:  = 1250, Ha:  > 1250
D) cannot be specified without knowing the size of the sample used by the engineer.
26. In a test of significance, the probability, assuming the null hypothesis is true, that the test statistic will take a value
at least as extreme as that actually observed is
A) the P-value of the test
B) the level of significance of the test
C) the probability the null hypothesis is true
D) the probability the null hypothesis is false
27. In testing hypotheses, which of the following would be strong evidence against the null hypothesis?
A) using a small level of significance
B) using a large level of significance
C) obtaining data with a small P-value
D) obtaining data with a large P-value
28. 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 
29.
A)
B)
C)
D)
In a test if statistical hypotheses, the P-value tells us
if the null hypothesis is true.
if the alternative hypothesis is true.
the largest level of significance at which the null hypothesis can be rejected.
the smallest level of significance at which the null hypothesis can be rejected.
30. We test the null hypothesis H0:  = 10 and the alternative Ha:  < 10 for a normal population with  = 4. A
random sample of 16 observations is drawn from the population and we find the sample mean of these
observations is J = 12. The P-value is closest to
A) 0.0228
B) 0.0456
C) 0.10
D) 0.9772
33. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams)  and
standard deviation  = 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 gave a mean of J = 1.53. Is this evidence that the
mean nicotine content is actually higher than advertised? To answer this, test the hypotheses
H0:  = 1.5, Ha:  > 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) that there is a 5% chance that the null hypothesis is true.
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35. The time needed for college students to complete a certain paper-and-pencil maze follows a normal distribution
with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time  is changed by
vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then
complete the maze. You compute the average time J that it takes these students to complete the maze and test the
hypotheses H0:  = 30, Ha:   30 You find that the results are significant at the 5% level. You may also conclude
A) that the test would also be significant at the 10% level
B) that the test would also be significant at the 1% level
C) both of the above
D) none of the above
36. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is J = 150
bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with
unknown mean  and that a 95% confidence interval for  is found to be 150  3.29. Which is true?
A) A test of the hypotheses H0:  = 150, Ha:   150 would be rejected at the 0.05 level
B) A test of the hypotheses H0:  = 150, Ha:  > 150 would be rejected at the 0.05 level
C) A test of the hypotheses H0:  = 160, Ha:   160 would be rejected at the 0.05 level
D) No hypothesis test can be conducted because we do not know 
40. 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 that
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) 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
41. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new
bulb has a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect
was statistically significant. The explanation is
A) that new designs typically have more variability than standard designs
B) that the sample size is very large
C) that the mean of 1200 is large
D) all of the above
45. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The mean
lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the
difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically
significant at the 0.05 level. If, in fact, there is no difference between the mean lifetimes of the new and old
designs, the researcher has
A) committed a type I error
B) committed a type II error
C) a probability of being correct equal to the P-value
D) a probability of being correct equal to 1 – (P-value)
47. A researcher plans to conduct a test of hypotheses at the 1%. She designs her study to have a power of 0.90 at a
particular alternative value of the parameter of interest. The probability she commits a type I error is
A) 0.01
B) 0.10
C) 0.90 D) equal to the P-value and cannot be determined until the data have been collected
49. Which of the following will increase the value of the power in a statistical test of hypotheses?
A) increase the significance level increase the sample size
C) consider computing the power for a value of the alternative that is farther from the value of the parameter of
interest under the null hypothesis
D) all of the above
50. A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a
power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will
commit a type II error for the particular alternative value of the parameter at which she computed the power is
A) 0.01 B) 0.10 C) 0.90 D) equal to the 1 – (P-value) and cannot be determined until the data have been collected
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51. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams)  and
standard deviation  = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but you are
suspicious and plan to investigate the advertised claim by testing the hypotheses H0:  = 1.5, Ha:  > 1.5 at the
5% significance level. You will do so by measuring the nicotine content of 100 randomly selected cigarettes of this
brand and computing the mean nicotine content J of your measurements. The power of your test at  = 1.6 is
A) 0.7995
B) 0.8413
C) 0.95
D) greater than 0.999
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Answer Key
1.
2.
6.
7.
8.
10.
11.
16.
17.
18.
23.
24.
26.
27.
28.
29.
30.
33.
35.
36.
40.
41.
45.
47.
49.
50.
51.
C
D
B
C
A
A
D
C
C
C
B
B
A
C
C
D
D
A
A
C
B
B
A
A
D
B
D
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