Name:
Test 3
Score:
/50
1. The Dell Computer Corporation claims that the average lifetime of the battery of a Dell Mini
9 netbook computer is 900 cycles (a cycle is a complete charge and discharge). We test 10
such batteries and find that the average number of cycles for this sample is 872.3. Which is
the appropriate pair of hypotheses to test Dell’s claim?
[4]
H0 :
Ha :
2. Suppose that we do a hypothesis test of the following pair of hypotheses:
[2]
H0 : p = 0.1
Ha : p =
6 0.1
If we compute our test statistic and find that the P -value of our test statistic is 0.43, which
of the following is the most accurate way to state our conclusion?
(a) We have very strong evidence that the null hypothesis is false.
(b) We have moderately strong evidence that the null hypothesis is false.
(c) We do not have enough evidence to say that the null hypothesis is false.
(d) We have strong evidence that the null hypothesis is true.
3. Indicate whether each of the following is true of false by circling the appropriate letter.
T F
T F
T F
T F
T F
T F
[6]
If a value of a test statistic is significant at the 1% level it is significant at the 5% level.
If the sample size is 10 and the value of the t-statistic for testing a hypothesis about the
mean is 2.45, we can say P < .01.
It is best to assign subjects randomly to each level of a blocking variable.
We should only use the “plus-four” confidence interval if the sample size is very large.
Suppose that µ = 9 and that we are testing the null hypothesis that H0 : µ = 10. Suppose
also that x̄ = 9.5. We will certainly reject the null hypothesis in this case.
If the P -value of a test statistic is .98 we can be fairly confident that H0 : is true.
4. Just yesterday, an article in the Sunday Times (London) reported on a study that showed
that
Students who routinely use Facebook have lower grades than those who do not.
The headline on an article reporting on this study read “Facebook impacts studies”. What is
wrong with the headline?
[2]
Name:
Test 3
Score:
/50
5. Suppose that an IRS examiner chooses a random sample of 100 income tax returns from
residents of Grand Rapids and find that 4 of them contain mistakes in reporting income.
Construct a 95% confidence interval for the percentage of all Grand Rapids returns that have
such mistakes.
[8]
6. A method currently used by doctors to screen women for possible breast cancer fails to detect
cancer in 15% of the women who actually have the disease. A new method has been developed
that researchers hope will be able to detect cancer more accurately. A random sample of
seventy women known to have breast cancer was screened using the new procedure. Of these,
the new method failed to detect cancer in six of the women. We want to determine if the new
procedure is better. Crunchit output, with strategic erasures, is below.
[4]
(a) Write the appropriate hypothesis:
H0 :
Ha :
(b) The researchers set a desired significance level of .05. Is the result statistically significant
at this level? (You can determine an approximate P -value from the given output.)
Name:
Test 3
Score:
/50
7. Each day, the Gallup Corporation asks a random sample of Americans whether they are
satisfied with the state of the nation. Yesterday, 1020 Americans participated in the survey
and 964 (68%) said yes. In the blanks below, write the symbol that we usually use to denote
that number in the story:
1,020
964
[3]
68%
8. In the United States, men are more likely to have lung cancer than women.
[5]
(a) Identify the explanatory and response variables in this description of data. Also indicate
the type of each (categorical or quantitative) and the possible values of each.
Explanatory Variable:
Type
Values
Response Variable:
Type
Values
(b) Why can’t we conclude that the relationship between these variables is causal?
9. A clinical trial is currently recruiting participants to test whether a certain kind of laser
treatment works to cure toenail fungus. They would like to test 40 participants. Twenty
participants will receive this new laser treatment and twenty participants will stick their foot
in the machine but there will be no laser treatment given to them. The technician will know
which participants receive the laser treatment and which are not really getting the treatment.
Choose whichever of the following terms would describe this experiment:
(a) completely randomized
(b) block design
(c) matched pairs
(d) unblinded
(e) single-blind
(f) double-blind
(g) placebo-controlled
[3]
Name:
Test 3
Score:
/50
10. Calvin just opened the annual web-based alumni survey. This survey is for graduates of the
three classes: 2008, 2004, and 1999. It is extraordinarily difficult to get Calvin alumni to
respond to this survey. In an effort to see what might increase response rate, we are testing
two methods. Some alumni will receive a postcard telling them about the survey and others
will receive a letter from the Provost. We conjecture that the response rate for those who
receive the letter will be higher that the response rate for those who receive a postcard. 1000
alumni will be included in this experiment.
(a) Identify:
Explanatory variable:
Response variable:
(b) Explain how you would carry out a completely randomized experiment for this study.
(c) Describe an experimental design that would improve the design in (a) by blocking.
(d) Why is the design you described in (b) an improvement over the design in (a)?
[7]
Name:
Test 3
Score:
/50
11. A certain battery is advertised as having an average lifetime of 150 hours. You want to test
that hypothesis. A random sample of batteries is tested. The data and Crunchit output from
a hypothesis test is given.
(a) How many batteries were tested?
(b) What is the value of the standard deviation of the sample?
(c) Using the result of this hypothesis test, write a statistical conclusion about the claim of
the advertisement. This conclusion should be a complete English sentence which uses
the statistical language appropriately.
[6]