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30 points
Statistics 108, Exam 3, Fall 2008
Name (print):_____________________
I confirm that I am allowed only a calculator and one 3-by-5 inch note card of notes for this exam. I will not look at
anybody else’s exam and I will take all necessary efforts to prevent others from seeing my exam. The consequence
of using additional test aids, copying from others, or allowing others to copy my work will result in disciplinary
action.
I have read and agree with the above statement. (If not see instructor.)
Signature: _____________________
1)
2pts. True or False: The calculation of a p-value is performed under the assumption that the null
hypothesis is true.
2) 2pts.Circle which statement best defines “95% confidence interval for the mean”.
 The 95% confidence interval is an interval that will include 95% of the data.
 If the sampling process were repeated 100 times and the 95% confidence interval
calculated for each sample, about 95 of the 100 sample means would be inside their
respective 95% confidence interval.
 The 95% confidence interval is a fixed interval calculated so that the population mean,
which is random, will fall within the interval about 95% of the time.
 If the sampling process was to be repeated 100 times and the 95% confidence interval
calculated for each sample, about 95 of the 100 confidence intervals will contain the
fixed population mean.
3) 2pts.Suppose a study was performed to investigate if the topical medicine (ProGain®) encourages
extra hair growth. 100 balding men volunteered for the study. The experimenters shaved the
volunteers’ heads and then the men were randomly assigned to two groups of 50. One group was
given a placebo and the other group given ProGain®. Being a blind study, the men did not know
which treatment they received. 2 months later, their heads were shaved again and the weight of
each man’s newly grown hair weighed. Circle which type of analyses would be best used for
this study.
 1-sample z-test
 1-sample t-test
 1-sample proportion
 Paired t-test
 2-sample t-test
4) 2pts.Suppose a study was performed to investigate if a computer software package could analyze
voices and have a better-than-random chance of deciding if a person is lying. 200 different
people’s voices were recorded while they stated the month that they were born. Half the people
were told to lie and half told to tell the truth. The researchers then looked at how many times, out
of those 200 trials, that the computer decided correctly whether or not the person had lied. Circle
which type of analyses would be best used for this study.
 1-sample z-test
 1-sample t-test
 1-sample proportion
 Paired t-test
 2-sample t-test
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5) 2pts. Referring back to the ProGain® study, suppose that ProGain® truly does encourage more
hair growth. Unfortunately, the statistics had the experimenters conclude that there was
statistically insignificant evidence (keep null hypothesis) that ProGain® encourages hair growth.
What type of error did they make?
6) 2pts. Circle which statement best defines a p-value.
 The p-value is the probability of the null hypothesis being true.
 The p-value is the probability of the alternative hypothesis being true.
 The p-value is the probability of committing a type 1 error.
 The p-value is the probability of committing a type 2 error.
 Assuming the null hypothesis is true, the p-value is the probability of getting a test
statistic as extreme or more extreme than the test statistic you calculated from your
sampled data.
 Assuming the alternative hypothesis is true, the p-value is the probability of getting a test
statistic as extreme or more extreme than the test statistic you calculated from your
sampled data.
7) Suppose a researcher studied the body temperatures of 27 students taking an exam. Using a level
of significance of 5% (α=0.05), the researcher performed a 1-sample t-test to test the null
hypothesis 𝐻0 : 𝜇 = 98.6 against the alternative hypothesis𝐻𝑎 : 𝜇 > 98.6.
a) 2pts. State the critical value(s) for this test.
b) 2pts. Suppose the null hypotheses were true, what would be the probability of rejecting
the null hypothesis?
c) 2pts. Suppose a statistical test was performed and the resulting p-value was 0.19. Should
you keep or reject the null hypothesis?
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8) 4pts. Suppose a researcher collected 22 juvenile rainbow trout and measured their lengths. Their
mean length was 35cm with a standard deviation of 5cm. Calculate a 95% confidence interval for
the mean length of juvenile rainbow trout.
9) Suppose you did a t-test 𝐻0 : 𝜇 = 𝜇0 vs. 𝐻𝐴 : 𝜇 ≠ 𝜇0 and your degrees-of-freedom was 10.
a) 2pts. State the critical value(s) for this test.
b) 2pts. Suppose the t-statistic was 1.37. Calculate the p-value.
10) 4pts. A biologist planted 400 seeds of a new type of corn. 320 of the seeds germinated. Assume
independence between seeds and that each has the same probability of germinating. Calculate a
95% confidence interval for the probability of a seed germinating (population proportion). Show
the formula you used.