Multiple Choice.
1. Which set of hypotheses is correctly written?
(a) H
0
: µ = 0 vs. H a
: µ 
0
(b) H
0
: x = 0 vs. H a
: x

0
(c) H
0
: µ < 0 vs. H a
: µ = 0
(d) H
0
:

= 0 vs. H a
: p > 0
(e) None of the above.
2.
In a test of H
0
: µ = 100 against H a
: µ 
100, a sample of size 80 produces z = 0.8 for the value of the test statistic. The P -value of the test is thus equal to:
(a) 0.20 (b) 0.40 (c) 0.29 (d) 0.42 (e) 0.21
3.
A 95% confidence interval for µ is calculated to be (1.7, 3.5). It is now decided to test the hypothesis
H
0
: µ = 0 vs. H a
: µ 
0 at the

= 0.05 level, using the same data as was used to construct the confidence interval.
(a) We cannot test the hypothesis without the original data.
(b) We cannot test the hypothesis at the

= 0.05 level since the

= 0.05 test is connected to the
97.5% confidence interval.
(c) We would fail to reject H
0
at level

= 0.05.
(d) We would reject H
0
at level

= 0.05.
(e) We would accept H
0
at level

= 0.05.
4.
The p-value of a significance test does not allow you to reject a hypothesis H0 in favor of an alternative Ha at the 5% level of significance. What can you say about significance at the 1% level?
(a) H0 can be rejected at the 1% level of significance.
(b) There is insufficient evidence to reject H0 at the 1% level of significance.
(c) There is sufficient evidence to accept H0 at the 1% level of significance.
(d) Ha can be rejected at the 1% level of significance.
(e) The answer can’t be determined from the information given.
5.
The weights of 10 apples have mean 7 ounces and standard deviation 0.4 ounces. What is the standard error of the mean?
(a) 0.40 (b) 0.04 (c) 0.13 (d) 2.80 (e) None of the above
6. The value of z* required for a 70% confidence interval is
(a) -0.5244
(b) 1.036
(c) 0.5244
(d) 0.6179
(e) The answer can’t be determined from the information given.


7. 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 that
(a) There is a 95% probability that

is between 6 and 12.
(b) There is a 95% probability that the true mean is 9 and a 95% chance the true margin of error is 3.
(c) 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) If we took many, many additional random samples and from each computed a 95% confidence interval for

, 95% of them would cover the values from 6 to 12.
(e) All of the above.
8. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct?
(a) The intervals have the same width.
(b) The 99% interval is narrower and has a greater chance of being incorrect.
(c) The 99% interval is wider and has a smaller chance of being incorrect.
(d) The 99% interval is narrower and has a smaller chance of being incorrect.
(c) The 99% interval is wider and has a greater chance of being incorrect.
9.
A 95% confidence interval for the mean reading achievement score for a population of thirdgrade students is (44.2, 54.2). The margin of error of this interval is
(a) 95%
(b) 5
(c) 2.5
(d) 10
(e) The answer cannot be determined from the information given.
10.
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 x of the weighings is computed.
Suppose the scale readings are normally distributed with unknown mean

and standard deviation

= 0.01 g. 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) 27061 (d) 10000 (e) 38416
11.
You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is
(a) 1.96
(b) 1.645
(c) 1.699
(d) .90
(e) 1.311



12.
The effect of acid rain upon the yield of crops is of concern in many places. In order to determine baseline yields, a sample of 13 fields was selected, and the yield of barley
(g/400m 2 ) was determined. The output from SAS appears below:
QUANTILES(DEF=4) EXTREMES
N 13 SUM WGTS 13 100% MAX 392 99% 392 LOW HIGH
MEAN 220.231 SUM 2863 75% Q3 234 95% 392 161 225
STD DEV 58.5721 VAR 3430.69 50% MED 221 90% 330 168 232
SKEW 2.21591 KURT 6.61979 25% Q1 174 10% 163 169 236
USS 671689 CSS 41168.3 0% MIN 161 5% 161 179 239
CV 26.5958 STD MEAN 16.245 1% 161 205 392
A 95% confidence interval for the mean yield is:
(a)
220.2 ± 1.96(58.6)
(b)
220.2 ± 1.96(16.2)
(c)
220.2 ± 2.18(58.6)
(d)
220.2 ± 2.18(16.2)
(e) 220.2 ± 2.16(16.2)
13.
The heights (in inches) of males in the United States are believed to be normally distributed with mean µ . The average height of a random sample of 25 American adult males is found to be x = 69.72 inches and the standard deviation of the 25 heights is found to be s = 4.15. The standard error of x is
(a) 0.17
(b) 0.69
(c) 0.83
(d) 1.856
(e) 2.04
14. Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence interval will have a width of 0.06?
(a) 748
(b) 1,068
(c) 1,503
(d) 2,056
(e) 2,401
15. A random sample of 900 individuals has been selected from a large population. It was found that 180 are regular users of vitamins. Thus, the proportion of the regular users of vitamins in the population is estimated to be 0.20. The standard error of this estimate is approximately:
(a) 0.1600
(b) 0.0002
(c) 0.4000
(d) 0.0133
(e) 0.0267
16. In a test of H
0
:

= 4 against H a
:
 
4, a sample of size 100 produces x

P -value (or observed level of significance) of the test is approximately equal to:
(a) 0.841 (b) 0.421 (c) 0.100 (d) 0.048 (e) 0.024
4 .
5 and s = 2.5. Thus the

17. The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with quotes of their responses are printed in the paper. Students are interviewed by a reporter “roaming” the campus selecting students to interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. Four of the students say no. Which of the following conditions for inference about a proportion using a confidence interval are violated in this example?
(a) The data are an SRS from the population of interest.
(b) The population is at least ten times as large as the sample.
(c) n p

10 and n ( 1
 p )

10 .
(d) No condition has been violated.
(e) More than one condition is violated.
18. In a test of the hypothesis H o
: µ = 100 versus H a
: µ > 100, the power of the test when µ = 101 would be greatest for which of the following choices of sample size n and significance level α?
(a) n = 10, α = 0.05
(b) n = 10, α = 0.05
(c) n = 10, α = 0.05
(d) n = 10, α = 0.05
(e) It cannot be determined from the information given
Free Response. (Remember that it is understood that you should follow the inference toolbox on all inference questions- confidence interval or significance test.) Use extra paper if needed.
19.A steel mill’s milling machine produces steel rods that are supposed to be 5 cm in diameter.
When the machine is in statistical control, the rod diameters vary according to a normal distribution with mean µ = 5 cm and standard deviation

= 0.02 cm. A large sample of 150 produced by the machine yields a sample mean diameter of 5.005 cm.
(a) Construct a 99% confidence interval for the true mean diameter of the rods produced by the milling machine.
(b) Does the interval in (a) give you reason to suspect that the machine is not producing rods of the correct diameter? Explain.

19.The level of dissolved oxygen in a river is an important indicator of the water’s ability to support aquatic life. You collect water samples at 15 randomly chosen locations along a stream and measure the dissolved oxygen. Here are your results in milligrams per liter:
4.53, 5.04, 3.29, 5.23, 4.13, 5.50, 4.83, 4.40, 5.42, 6.38, 4.01, 4.66, 2.87, 5.73, 5.55
Construct a 95% confidence interval for the mean dissolved oxygen level for this stream.
20.Patients with chronic kidney failure may be treated by dialysis, using a machine that removes toxic wastes from the blood, a function normally performed by the kidneys. Kidney failure and dialysis can cause other changes, such as retention of phosphorous, that must be corrected by changes in diet.
A study of the nutrition of dialysis patients measured the level of phosphorous in the blood of several patients on six occasions. Here are the data for one patient (milligrams of phosphorous per deciliter of blood):
5.6 5.3 4.6 4.8 5.7 6.4
The measurements are separated in time and can be considered an SRS of the patient’s blood phosphorous level. Assume that this level varies normally. The accepted range of phosphorous in the blood is considered to be 2.6 to 4.8 mg/dl. a)Is there strong evidence that the patient has a mean phosphorous level that exceeds 4.8? b) Describe Type I and Type II errors in this situation. Which one has a more serious consequence? c) Describe power in this situation.
21 A candidate for mayor claims that under the present administration, 45% of complaints about city government are not addressed within two weeks of submission. A watchdog citizens’ group conducted a simple random sample of 50 complaints submitted to the city government in the last year and determined that only 40% of the complaints were not addressed within two weeks of submission. Do these data provide sufficient evidence to reject the candidate’s claim at the 5% significance level? Answer the question using both a confidence interval and a significance test.