The document reviews statistical concepts and tests related to hypothesis testing and inferences from two samples. It includes practice problems and scenarios such as testing drug failure rates among job applicants, comparing bear weights, and analyzing differences in calorie counts between yogurt brands. Additional examples cover research on directional asymmetry in flies and the impact of pollution on the health of snake species.

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Statistics, Sample Test (Exam Review)
Module 4: Chapters 8 & 9 Review
Chapters 8: Hypothesis Testing
Chapters 9: Inferences from Two Samples
Chapters 8: Hypothesis Testing
1. Answer the following:
a. A test of hypothesis is always about a population ______________
b. The observed value of a test statistic is the value ________ for a sample
statistic.
c. As the sample size gets larger, both type I and type II errors decrease or
increase?
d. Define type I error.
e. Define type II error.
f. The value of  is called the ______________
g. The value of  is called the ______________
h. The value of 1 
− is called the ______________
2. In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01
significance level, test the claim that the failure rate is now lower if a simple random
sample of 1520 current job applicants result in 58 failures. Does the result suggest
that fewer job applicants now use drugs?
a) State the null and alternative hypothesis.
b) Calculate the value of test statistic.
c) Find the critical value.
d) Make a decision.
e) Find the p-value & make a decision. Is this decision in agreement with the
previous one?
f) What is type I error, what is the probability of making type I error.
3. A sample of 54 bears has a mean weight of 182.9 lb. Let’s assume that the standard
deviation of weights of all such bears is known to be 121.8 lb, at 0.1
 = , is there
enough evidence to support the claim that the population mean of all such bear
weights is less than 200 lb?
a. State the null and alternative hypothesis.
b. Calculate the value of test statistic.
c. Find the critical value(s).
d. Make a decision.
4. Sixteen new textbooks in the college bookstore, had prices with a mean of $70.41 and
a standard deviation of $19.70. Use a 0.05 significance level to test the claim that the
mean price of a textbook at this college is less than $75? Assume normal population.

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5. Tests in the author's past statistics classes have scores with a standard deviation equal
to 14.1. One of his current classes now has 27 test scores with a standard deviation of
9.3. Use a 0.01 significance level to test the claim that this current class has less
variation than past classes. Does a lower standard deviation suggest that the current
class is doing better? Assume the population is normal.
6. Consider a population of frogs living on an island. We believe that the
frogs may be members of a species called Rana Pipiens. The mean length
of Rana Pipiens is known to be 11cm.
The following length values (cm) were obtained for a sample of
individuals from the island:
10.6 11.2 10.6 9.9 10.7 9.8 10.1 9.6 12.5 11.2 10.3
10.1 8.9 11.1 9.3 11.9 9.7 11.5 10.3 11.2
Do these frogs have sizes that are consistent with them being Rana
Pipiens or not? Are these frogs Rana Pipiens or not? Use a 0.05
significance level.
Statistics, Sample Test (Exam Review)
Module 4: Chapters 8 & 9 Review
Chapters 9: Inferences from Two Samples
1. Among 843 smoking employees of hospitals with the smoking ban, 56 quit smoking
one year after the ban. Among 703 smoking employees from work places without
the smoking ban, 27 quit smoking a year after the ban.
a. Is there a significant difference between the two proportions? Use a 0.01
significance level.
b. Construct the 99% confidence interval for the difference between the two
proportions.
2. Company ''A'' claims that its yogurt cups contain, on average fewer calories than
that of a competitor. A sample of 50 such yogurt cups of company ''A'' produced
an average of 141 calories per cup with a standard deviation of 5.4 calories. A
sample of 40 yogurt cups of a rival company “B” produced an average of 144
calories per cup with a standard deviation of 6.3 calories.
a. Assuming that the calories of the yogurt cups for company “A” and company
“B” have Different Variances, use a 0.01 significance level to test the claim.
b. Calculate the p-value for the test of previous part & make a decision. Is this
decision in agreement with the previous one?

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c. Make the 98% confidence intervals for the difference between the two means.
3. Assuming that the calories of the yogurt cups for company “A” and company “B”
have Equal Variances, repeat the previous question.
4. Test a claim that weights of male college students have a larger variance than
female college students. (Use a significance level of 0.05 and assume the
populations are normal.)
: 31, 168, 28,
: 29, 125, 25
Males n x s
females n x s
= = =
= = =
5. Directional asymmetry (DA) is a phenomenon whereby in a population one side of
each organism is consistently larger than the other (I.E., left larger than right). An
evolutionary biologist studying DA measures the length of the left and right wings of
a sample of Drosophila (a type of flies, whose members are often called “small fruit
flies”) collected from nature and she gets these data.
a. The researcher decides to perform a two-sample t test to determine whether
the mean wing differs between the left and right sides of these flies. What
type of t test will she do? α = 0.05
b. Find the 90% confidence interval for the difference between the means.
Fly ID #
Length (MM)
Left wing
Length (MM)
Right wing
1 1.34 1.26
2 1 1.28
3 1.09 1.36
4 1.06 1.25
5 1.15 1.33
6 1.35 1.38
7 1.26 1.16
8 1.09 1.04
9 1.01 1.4
10 1.31 1.1
11 1.35 1.02
12 1.02 1.47
13 1.26 1.12
14 1.32 1.46

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15 1.29 1.24
16 1.02 1.41
17 1.2 1.38
6. An ecologist is concerned with whether pollution entering part of a preserve area is
compromising the health and growth of an endangered species of snake. To
determine this, he decides to measure the length of a set of mature adults from the
polluted area and an unpolluted area. The researcher decides to perform a two-
sample t test to determine whether the mean length of these snakes differs
between these two areas. α = 0.05
Length measurements
unpolluted area (cm)
Length measurements
polluted area (cm)
1 27 25
2 28 26
3 30 28
4 29 27
5 28 23
6 28 21
7 28 19
8 31 28
9 25 23
10 23 24
11 21 26
12 26 28
13 28 25
14 30 26
15 27 25
16 21
17 24