Download 10 1 and 10 2 Review 3 Answers

AP Statistics
Chapter 10 Review
Name __________________________________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1. If the 90% confidence interval of the mean of a population is given by 45  3.24 , which of the following is correct?
(a) There is a 90% probability that the true mean is in the interval.
(b) There is a 90% probability that the sample mean is in the interval.
(c) If 1,000 samples of the same size are taken from the population, then approximately 900 of them will contain the true mean.
(d) There is a 90% probability that a data value, chosen at random, will fall in the interval.
(e) None of the above.
2. Which of the following will reduce the width of a confidence interval?
I.
Increasing the confidence level.
II.
Increasing the sample size.
III.
Decreasing the standard deviation.
(a)
(b)
(c)
(d)
(e)
I only
I and II only.
II and III only.
I, II, and III.
None of the above.
3. Which of the following is true?
(a) A highly significant result indicates that the sample result never really happened.
(b) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good
indication that bias must have been involved with the data collection.
(c) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good
indication that the value of the parameter could be significantly different than what is stated.
(d) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good
indication that whoever stated the expected value is lying.
(e) None of the above.
4. The P-value of a test of significance is the probability that:
(a)
(b)
(c)
(d)
(e)
The decision resulting from the test is correct.
95% of the confidence intervals will contain the parameter of interest.
The null hypothesis is true.
The alternative hypothesis is true.
None of the above.
5. The confidence that we feel about a 90% confidence interval comes from the fact that
(a)
(b)
(c)
(d)
(e)
there is a 90% chance that the population parameter is contained in the confidence interval.
there is a 90% chance that the sample statistic is contained in the confidence interval
90% of the confidence intervals constructed around a sample statistic will contain the population parameter
the terms confidence and probability are interchangeable
the concepts of confidence and probability are synonymous
6. What sample size should be chosen to find the mean number of absences per month for school children to within .2 at a 95%
confidence level if it is know that the standard deviation is 1.1?
(a)
(b)
(c)
(d)
(e)
11
29
82
96
117
7. What assumptions are necessary to validate a 95% confidence interval from a sample size 6 of the form:
I.
II.
III.
(a)
(b)
(c)
(d)
(e)


?
   x  1.96
6
6
The sample must have been randomly drawn from the population.
The population is approximately normal.
The population standard deviation must be known.
x  1.96
I only.
I and II only.
I and III only.
I, II, and III.
None of the above.
8. In general, how does doubling the sample size change the confidence interval size?
(a) Doubles the interval size.
(b) Halves the interval size.
(c) Multiplies the interval size by
2.
(d) Divides the interval size by 2 .
(e) Cannot be determined without knowing the sample size.
9.
Under what conditions would it be meaningful to construct a confidence interval estimate when the data consists of the entire
population?
(a) If the population size is small  n  30 
(b) If the population size is large  n  30 
(c) If a higher level of confidence is desired
(d) If the population of truly random
(e) Never
10. A pharmaceutical company executive claims that a medication will produce a desired effect for a mean time of 58.4 minutes. A
government researcher runs a hypothesis test of 250 patients and calculates a mean of 59.5. If the population standard deviation is
known to be 7.6, in which of the following intervals is the P-value located?
(a)
(b)
(c)
(d)
(e)
P < .01
.01 < P <.025
.025 < P < .05
.05 < P < .10
P > .10
2
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
11. A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. A study was done
on maximal heart rate of 9 randomly selected male triathletes. The results were:
x
Swimming
Biking
Running
a.
188
186
194

7.2
8.5
7.8
Assuming that the heart-rate distribution for each event is approximately normal, construct 95% confidence intervals for the true
mean heart rate of triathletes for each event.
Swimming (183.3, 192.7)
Biking (180.45, 191.55)
Running (188.9, 199.1)
b.
Do the intervals in part a overlap? Based on the computed intervals, do you think there is evidence that the mean heart rate for
running is higher than the other two events? Explain.
The intervals do overlap. However, the interval for running is much higher than for the other 2 events. It is 5 heartbeats higher than
swimming, and about 7 heartbeats faster than for swimming. This may be evidence that the mean heart rate for running is higher than
for biking or swimming.
1.
12. According to numbers published by Nielsen, a certain program has popularity rating of 35 (based on the percent of people
watching the show). We suspect that the rating is not accurate. In conducting a sample of 100 randomly selected television
viewers, we find that the sample popularity rating is 30. We know that the population standard deviation is 8.2.
a) Find a 99% confidence interval for  and state, in plain English, what it tells you.
C99 = (27.88768, 32.11232)
We are 99% confident that the true mean popularity rating for this program lies in the interval from 27.88768 to 32.11232.
b) Conduct a hypothesis test at the .01 level of significance using the confidence interval calculated in part a.
µ is the true popularity rating for certain shows.
Ho: µ = 35
Ha: µ ≠ 35
Assumptions
SRS is given
Normality of the sampling distribution is approximated by sample size
Sigma is known.
Calculations:
z* = 2.576 C99 = (27.88768, 32.11232)
Conclusion:
Since our interval doesn’t contain the rating of 35, the result is significant and we reject Ho. There is
evidence to believe that the true rating of this program may not be 35.
3
12. A pharmaceutical manufacturer does a chemical analysis to check the potency of products. The standard release potency for
cephalothin crystals is 910 (   8.2 ) and the manufacturer believes this claim may be too high. An assay of 16 lots gives the
following potency data:
897
918
a.
914
906
913
895
906
893
916
908
918
906
905
907
921
901
Test the manufacturer’s claim at the 0.01 level of significance.
µ = 910, sigma = 8.2 n = 16 x  907.75
 =.01
µ = the true standard release potency for cephalothin crystals.
Ho: µ = 910
Ha: µ < 910
Assumptions: SRS is assumed, not given.
Normality of the sampling distribution is verified graphically.
Sigma is known.
Calculations:
z
907.75  910
 1.0976
8.2
16
P ( z < -1.0976) = normalcdf (-1e99, -1.0976) = .1362
Conclusion: Since p > a, the results are not significant and we fail to reject Ho. There is not sufficient evidence to believe the true
mean release potency for cephalothin crystals is less than 910.
4