Updated Fall 2011
Intro to Stats, Test 2 Review
Name ______________________________
Section A: Which Test to Run?
For each of the following research scenarios, select the appropriate statistical test.
1. Researchers are wondering if hypertension and smoking are related. They divide their 500
participants into 3 groups: non-smokers, moderate smokers and heavy smokers. They
measure the blood pressure of the participants in each category.
Z-Interval
T-
-
-
-Test (Ind. Samples)
-Test
ANOVA
2. The following data represents the running time of recent movies from two top motion-picture
companies. Test the hypothesis that company 2’s movies have on average a longer running
time.
Company
Running Time (Minutes)
1
102 86 98 109 92
2
81 165 97 134 92 87 114
-Interval
-
-
-Test (Dep. Samples)
-
-Test
3. A college infirmary conducted an experiment to determine the degree of relief provided for
each of three cold remedies: NyQuil, Robitussin and Triaminic. They had 30 students with
colds. Ten students tried each remedy and reported the level of relief they experienced on a
scale of 1 – 10 with 10 being perfect relief and 1 being no relief.
-Interval
-
-
-Test (Dep. Samples)
-
-Test
4. To determine if a new serum will arrest leukemia, 9 mice with advanced leukemia are
selected, 5 of which receive the serum, 4 of which do not. Survival times (in months) are
recorded.
-Interval
-
-
-
-
-Test
5. A manufacturer of rice cereal (baby food) claims the average fat content does not exceed 1.5
milligrams per serving. A consumer group purchases 40 jars of the food and tests the
average fat content. They are concerned that the food has a higher fat content than
advertised.
-Interval
-
-
-Test (Dep. Samples)
-
-Test
6. Joe and Moe are two Marine Corps drill instructors at Quantico, VA. Joe doesn’t think Moe
works his Officer Candidate School (OCS) classes hard enough. Moe gives all 25 of his
OCS candidates a physical fitness when they arrive. The same test is repeated after 4 weeks
of Moe’s gentle persuasions.
-Interval
-
-
-
-
-Test
7. Dr. Sinn queries his students about their flip flop ownership. He is trying to estimate the
percentage of his students who have more than 5 pairs of flip flops.
-Interval
-
-Test
-
-
-Test
Updated Fall 2011
8. A large automobile manufacturer is deciding between two brands of tires to purchase for its
newly designed SUV. They test 50 sets of each type by putting sets of tires on the SUV’s
and driving them until the tires are worn out.
-Interval
-
-
-
-
-Test
9. A researcher surveys males and females about their preferences for corrective lenses. She
finds that 49 of 72 females who need corrective lenses prefer contacts, while 36 of 58 males
prefer contacts. She tests for a gender difference in preference for contacts at the .05 level.
-Interval
-
-
-
-
-Test
10. Researchers are testing 3 treatments for cold and flu symptoms, comparing them to each
other and to a control group that simply drinks lots of fluids. The average amount of relief is
measured for each group.
-Interval
-
-
-
-
-Test
11. Jack Erwin, professional fisherman extraordinaire, catches a large trout and nearly has the
doggone thing reeled in. He caught a 26” trout earlier that day that weighed in at a hefty 7.5
lbs, and this one looks even bigger. But then, doggone it, his 15 lb. test fishing line breaks,
and he suffers the agony of watching one get away. He purchases 10 more packages of
fishing line to test his hypothesis that the mean breaking strength of the fishing line is less
than the advertised 15 lbs. of force.
-Interval
-
-
-
-
-Test
12. Researchers were trying to determine if the material in a college physics course was better
understood by students when the course had an accompanying lab section. Of the 28
participants, 11 were randomly selected for the lab course and 17 for the course without a
lab. The exact same end-of-course test was administered to all 28.
-Interval
-
-
-
-
-Test
13. Joe and Moe, over beers in the NCO, decide to estimate the average fitness levels of
incoming OCS candidates. They give 100 future Marine Corps officers a physical fitness test
and estimate with a 95% level of confidence.
-Interval
-
-
-
-
-Test
14. Researchers in Boulder, CO, believe that running increases the percent resting heart rate
(RMR) in older women. The average RMR of 30 elderly women runners was higher than the
average RMR of 30 sedentary elderly women.
-Interval
-Interval
-
-
-
-Test
Updated Fall 2011
Section B: Symbolic Hypotheses, Error Rates and Choosing α
For each of the following research scenarios, (a) set up the null and alternate hypotheses in
correct mathematical symbols, (b) describe both Type I and II errors in words and (c)
choose an appropriate level for α.
15. Environmental engineering students at Georgia Tech have found a new way to cure concrete.
The old method (developed in Athens, Georgia) generated concrete with an average strength
of 5000 kg/cm2. They cure and test 42 samples. Statistically test the hypothesis that the new
curing method generates stronger cement.
16. Pharmaceutical researchers are testing allergy medications. Their new drug SuperCureAll
has some rather nasty side effects. They compare 31 adults with allergies who take
SuperCureAll to 22 adults with allergies who take a placebo. The allergy sufferers rate their
levels of relief from 1 – 10, 10 being complete relief. The placebo group average is 3.9.
17. A consumer advocacy group is testing the shock absorbency of an infant car seat they believe
may be defective. They purchase 12 of the seats whose mean absorbency is rated at 1000
lbs.
Updated Fall 2011
Section C: Hypothesis Testing
Conduct all relevant hypothesis testing steps for each of the following scenarios.
18. Dr. Olsen is concerned about her pH meter. She finds a neutral substance which should give
meter readings of 7.0 on the pH scale. She conducts 10 sample measurements (data given
below) of the substance on her balky meter. At the α = .1 level, test her hypothesis that the
meter is faulty. Assume normality.
7.07 7.0 7.1 6.97 7.0 7.03 7.01 7.01 6.98 7.08
19. You are a consultant for a manufacturer who asks you to compare the abrasive wear for two
types of lamination. For Laminate X, 12 pieces of material are tested and earn an average
rating of 85 on a scale of 0 - 100 where 100 indicates “no visible wear” and 0 indicates
“completely destroyed” (s.d. = 4). For Laminate Z, 10 pieces are tested and average an 81
(s.d. = 5). Given that the two laminates cost roughly the same to produce, test the hypothesis
that X is significantly better than Z at an appropriate level. Assume normality.
20. After Halloween, twins Jacob and Katie decide to see whose favorite color appears more
often in their favorite flavor. Katie thinks Green Peanut Butter M&M’s are the bomb, but
Jacob likes the classic M&M’s in the color Red. In a sample of 342 Peanut Butter M&M’s,
Katie find 52 Green ones. In a sample of 519 classic M&M’s, Jacob finds 95 Reds. Test the
hypothesis that Red M&M’s appear more often (in classic M&M packages) than Green
Peanut Butter M&M’s do.
Updated Fall 2011
21. Researchers are wondering if hypnosis will influence mathematics test anxiety. They give 9
students a mathematics test un-hypnotized. Three weeks later, the participants take the same
test after being hypnotized by a trained professional (do NOT try this at home!). Their scores
are given below. Test their hypothesis about hypnosis at the α = .05 level assuming
normality.
Test 1 58 67 79 59 66 71 70 52 65
Test 2 59 70 78 66 68 66 81 71 71
22. The following data represents the running time of recent movies from two top motion-picture
companies. Test the hypothesis that Company 2’s movies have on average a longer running
time at the α = .025 level. Assume normality.
Company
Running Time (Minutes)
1
102 86 98 109 92
2
81 165 97 134 92 87 114
23. Archaeology. Samples of head breadths were obtained by measuring skulls of Egyptian
males from three different epochs. Changes in head shape over time suggest inbreeding with
immigrant populations. Use a 0.05 level of significance to test the claim that head breadths
were different over time. Assume normality.
4000 B.C. 131 138 125 129 132 135 132 134 138
1850 B.C. 129 134 136 137 137 129 136 138 134
150 A.D. 128 138 136 139 141 142 137 145 137