Download Review for Test 2

Review for TEST II
Make sure to identify all elements of Test of Hypothesis and Confidence Interval, such as :
Point estimator, Sampling Error, Test statistic, Critical value, P-value, Rejection Region, Level of significance,
Error type I and II, Null and Alternate hypotheses, Assumptions.
Good luck!
1. A salesman for a shoe company claimed that runners would record quicker times, on the average, with the
company's brand of sneaker. A track coach decided to test the claim. The coach selected eight runners. Each
runner ran two 100-yard dashes on different days. In one 100-yard dash, the runners wore the sneakers supplied
by the school; in the other, they wore the sneakers supplied by the salesman. Each runner was randomly assigned
the sneakers to wear for the first run. Their times, measured in seconds, were as follows:
Sneakers 1
Company 10.8
School
11.4
2
12.3
12.5
3
10.7
10.8
4
12.0
11.7
5
10.6
10.9
6
11.5
11.8
7
12.1
12.2
8
11.2
11.7
Note. For the differences, X D = -.225 and s D = .276. Assume the population of differences is normal.
2. A new insect spray, type A, is to be compared with a spray, type B, that is currently in use. Two rooms of
equal size are sprayed with the same amount of spray, one room with A, the other with B. Two hundred insects
are released into each room, and after 1 hour the numbers of dead insects are counted." There are 120 dead
insects in the room sprayed with A and 90 in the room sprayed with B. Do the data provide enough evidence to
indicate that spray A is more effective than spray B? Use α = .05.
3. To compare two methods of teaching reading, randomly selected groups of elementary school children were
assigned to each of the two methods for a 6-month period. The criterion for measuring achievement was a
reading comprehension test." The 11 students assigned to method I had a mean score of 64 with a variance of 52.
The 14 students assigned to method II had a mean score of 69 with a variance of 71. Do the data provide enough
evidence to indicate a difference in the mean scores on the comprehension test for the two teaching methods?
Use α = .01.
4. Magnets are often used by people to treat a variety of disorders. Researchers recently treated a group of
patients with magnets and another group of patients with a fake magnet treatment. The results are given below.
Test the claim that the magnet treatment is more effective at lowering pain in arthritis patients:
Sample size
Mean Pain Reduction
Standard Deviation
Treatment Group
35
0.49
0.96
Placebo Group
35
0.44
1.4
5. A study at the University of Michigan wants to determine student options regarding non-revenue-generating
athletics. Specifically, one question in a survey asks students "Do you think the women's basketball program
should be discontinued?" The data collected revealed that 100 of the 1,000 females surveyed responded "Yes"
and that 400 of the 1,000 males surveyed responded "Yes". Suppose a 99% confidence interval resulted in the
following confidence interval for the true difference in population proportions: (-.5, -.1). Interpret the interval.
What is value of the point estimator? ______
What is the value of margin of error? _______
6. How does wives' employment status affect their husbands' well being? To answer this question, a survey of
the job satisfaction of 25 male accountants who were employed full-time and married was conducted. In this
sample, 15 wives were employed and 10 were unemployed. The goal of the study is to compare the mean job
satisfaction levels of the two groups of husbands: (1) those with working wives and (2) those with unemployed
wives. The observed significance level (p-value) of the test is .03. Is this sufficient evidence to conclude that the
mean satisfaction level of husbands with working wives is less than the mean satisfaction level of husbands with
unemployed wives? Test using  =.05.
7. In a study of the accuracy of telephone surveys, 720 people out of 1720 refused to respond during a standard
five day survey. In the same study, 429 people out of 1640 refused to respond during a rigorous eight week
survey. Use a 0.01 significance level to test the claim that the refusal rate is lower with the rigorous survey.
8. In a test of Ho: p1  p2  0 versus Ha: p1  p2  0 , the p-value=0.042. Use α = .03.
There is (sufficient / insufficient) evidence to conclude that P1 is (greater / less) than P2.
9. A weight-lifting coach claims that weight-lifters can increase their strength by taking a certain supplement. To
test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The
results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The
new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength.
Athlete
A
Before
215
After
225
Differences
B
240
245
C
188
188
D
212
210
E
275
282
F
260
275
G
225
230
H
200
195
I
185
190
10. Two brands of water filters are to be compared in terms of the mean reduction in impurities measured in parts
per million (ppm) . Twenty-one water samples were tested with each filter and reduction in the impurity level
was measured, resulting in the following data:
Filter 1: n1  21
x 1  8.0
s12  4.5
Filter 2: n2  21
x 2  6.5
s 22  2.0
Calculate and interpret the 95% confidence interval for the mean difference 1   2 between the two filters,
assuming  12   22 .
11. A study is been conducted to estimate the difference in time to complete a certain task by skilled and
unskilled workers. The resulting confidence interval is (-7.8 min, 12.3min). The data seem to provide evidence
that _______________ (there is, there is not) a significant difference in time between the two groups of workers.
12. The difference in yearly income for a certain professional occupation, between women and men has been
estimated by the interval $2,060 < μw − μm < $4,660. Thus the difference between the sample means was
_______________ and the margin of error was ________________
13. The weight reduction has been estimating in pair match design comparing the weight of each of 20
individuals before and after following a liquid diet for a week. The resulting estimation of the reduction in pound
was (6ponds, 13pounds). Do the data provide evidence of a difference between the two means?
14. Determine whether the samples are independent or consist of matched pairs.
• The effectiveness of Prilosec, for treating heartburn is testing by measuring gastric acid secretion. A group of
patients is treated with Prilosec and another group of patients given a placebo. ____________
• The effectiveness of Prilosec for treating heartburn is testing by measuring gastric acid secretion in patients
before and after the drug treatment. The data consists of the before/after measurements for each patient.
• The accuracy of verbal responses is tested in an experiment in which subjects report their weight and they are
then weighted on a physician’s scale. The data consists of the reported weight and the measured weight for each
subject. __________________
• The effect of sugar in an ingredient is tested with a sample of cans of regular Coke and another sample of cans
of diet Coke. ___________________
15. The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand
B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can
determined. The study provided the following summary information.
16.
Two independent samples (A and B) were selected from normally distributed populations which have
the same variance. Compute the value of the pooled variance estimator.
n
x
s2
A
12
143.4
12.4
B
12
148.9
11.6
17. Twenty-four males age 25-29 were selected from the Framingham Heart Study. Twelve were smokers and 12
were nonsmokers. The subjects were paired, with one being a smoker and the other a nonsmoker. Otherwise,
each pair was similar with regard to age and physical characteristics. Systolic blood pressure readings were as
follows:
A
Smokers
122
146
120
114
124
126
118
128
130
134
116
130
B
Nonsmokers
114
134
114
116
138
110
112
116
132
126
108
116
List the differences A - B and verify that X D = 6 and s D = 8.40. Use a 5% level of significance to determine
whether the data indicate a difference in mean systolic blood pressure levels for the populations from which the
two groups were selected. You may assume that the population of differences is approximately normal.
18. It is conjectured that classes that use a statistical computer package, such as Minitab, do better in
introductory statistics courses than those who don’t use such technology. A random sample of 24
students uses a statistical computer package while taking statistics. Another random sample of 28
students taking the same course uses only hand-held calculators. The final average in the course is
recorded for each of these students. These data are below.
Is there sufficient evidence to conclude that students who do not use the computer have lower
averages? Use a = .05.
19. A manufacturer of shock absorbers would like to advertise that their shock absorbers last longer
than those produced by its biggest competitor. To see if there is support for such a claim, six of the
manufacturer’s shocks and six of the competitor’s shocks were randomly selected, and one of each
brand was installed on the rear wheels of each of six cars. After the cars had been driven 20,000
miles, the strength of each shock absorber was measured. These data are below.
Is there sufficient evidence to conclude that the manufacturer’s shocks have a greater mean strength
after 20,000 miles of driving than the competitor’s? Use a .01 level of significance.
20. The personnel manager of a large retail clothing store suspects a difference in the mean amount of break time
taken by workers during the weekday shifts compared to that of the weekend shifts. It is suspected that the
weekday workers take longer breaks on the average. A random sample of 46 weekday workers had a mean 1 x1 =
53 minutes of break time per 8-hour shift. A random sample of 40 weekend workers had a mean x2 = 47 minutes.
Previous studies show that ó1 = 7.3 minutes and ó2 = 9.1 minutes. Test the manager’s suspicion at the 5% level
of significance.
21. An independent rating service is trying to determine which of two film developing ships has quicker service.
Over a period of 12 randomly selected times, the average waiting period to develop a 24-exposure roll sold at
Shop 1 is 58 minutes with standard deviation 3.5 minutes. The average waiting period at Shop 2 to develop a 24exposure roll over a period of 8 randomly selected times is 53 minutes with standard deviation 4.9 minutes.
Using a 1% level of significance, can we say there is a difference in the average waiting time at Shop 1 and Shop
2?
22. Two growth hormones are being considered. A random sample of 10 rats were given the first hormone and
their average weight gain was x1 = 2.3 pounds with standard deviation s1 = 0.4 pound. For the second hormone, a
random sample of 15 rats showed their average weight gain to be x2 = 1.9 pounds with standard deviation s2 =
0.2 pound. Assume the weight gains follow a normal distribution. Using a 10% level of significance, can we say
there is a difference in average weight gains for the two growth hormones?
Find a 90% confidence interval for the difference in average weight gains for the two growth hormones.
23. Stone Tires has developed a new tread which they claim reduces stopping distance on wet pavement. A
random sample of 56 test drives with cars using tires with tread type I (old design) showed that the average
stopping distance on wet pavement was x1 = 183 feet. A random sample of 61 test drives conducted under similar
conditions, but with cars using tires with tread type II (new tread) showed that the average stopping distance was
x2 = 152 feet. Historical data suggests ó1 = 49 feet and ó2 = 53 feet. Using a 1% level of significance, can we
support the claim?
Find a 90% confidence interval for the population mean difference µ1 - µ2 of stopping distances for the two
types of tire tread.
24. A local bank claims that the waiting time for its customers to be served is the lowest in the area. A
competitor's bank checks the waiting times at both banks. Test the local bank's claim. Use  = 0.05.
Local Bank
n1 = 15
X 1 = 5.3 minutes
S1 = 1.1 minutes
Competitor Bank
n2 = 16
X 2 = 5.6 minutes
S2 = 1.0 minutes
25. A local school district is concerned about the number of school days missed by its teachers due to illness. A
random sample of 10 teachers is selected. The number of days absent in one year is listed below. An incentive
program is offered in an attempt to decrease the number of days absent. The number of days absent in one year
after the incentive program is listed below. Test the claim that the incentive program cuts down on the number of
days missed by teachers. Use  = 0.05. Assume that the distribution is normally distributed.
Teacher
Days absent before incentive
Days absent after incentive
A
3
1
B
8
7
C
7
7
D
2
0
E
9
8
F
4
2
G
2
0
H
0
1
I
7
5
J
5
5
26. Is there a difference in the total scores for women’s and men’s basketball games? A random sample of
n1 = 55 women’s games had a mean winning score of x1 = 78. Another random sample of n2 = 60 men’s games
had a mean winning score of x2 = 90. Historical data suggests ó1 = 10 and ó2 = 16. Find a 95% confidence
interval for the population difference µ1 - µ2.
(a) -13.3 to -10.7
(b) -16.8 to -7.2
(c) -16.1 to -7.9
(d) -18.4 to -5.6
(e) -38.2 to 14.2
27. Two growth hormones are being considered. A random sample of 10 rats were given the first hormone and
their average weight gain was x1 = 2.3 pounds with standard deviation s1 = 0.4 pound. For the second hormone, a
random sample of 15 rats showed their average weight gain to be x 2 = 1.9 pounds with standard deviation s2 =
0.2 pound. Assume the weight gains follow a normal distribution. Find a 90% confidence interval for the
difference in average weight gains for the two growth hormones.
(a) 0.20 lb to 0.60 lb (b) 0.17 lb to 0.63 lb
(c) 0.24 lb to 0.56 lb (d) 0.175 lb to 0.625 lb (e) 0.15 lb to 0.65 lb
28. Stone Tires has developed a new tread which they claim reduces stopping distance on wet pavement. A
random sample of 56 test drives with cars using tires with tread type I (old design) showed that the average
stopping distance on wet pavement was x1 = 183 feet. A random sample of 61 test drives conducted
under similar conditions, but with cars using tires with tread type II (new tread) showed that the average stopping
distance was x2 = 152 feet. Historical data suggests ó1 = 49 feet and ó2 = 53 feet.
Find a 90% confidence interval for the population mean difference µ1 - µ2 of stopping distances for the two
types of tire tread.
a) 15.5 to 46.5
b) 13.5 to 44.5
c) 14.5 to 43.5
d) 16.5 to 45. 5
e) 12.5 43.5
29. At a large office supply store, the daily sales of two similar brand-name laser printers are being compared. A
random sample of 16 days showed that Brand I had mean daily sales x1 = $2464 with standard deviation
S1 = $529. A random sample of 19 days showed that Brand II had mean daily sales x 2 = $2285 with sample
standard deviation S2 = $440. Assume sales follow an approximately normal distribution.
Find a 90% confidence interval for the population mean difference in sales µ1 - µ2.
30. A random sample of 100 students at a high school was asked whether they would ask their father or mother
for help with a homework assignment in science. A second sample of 100 different students was asked the same
question for an assignment in history. Forty-three students in the first sample and 47 students in the second
sample replied that they turned to their mother rather than their father for help. Construct a 98% confidence
interval for PM - PF .
31. Consider a study conducted to compare the abilities of men and women to perform the strenuous tasks
required of a shipboard firefighter. The researchers measured the pulling force (in newtons) that a firefighter was
able to exert in pulling the starter cord of a P-250 water pump. Firefighters were matched in pairs according
to weight, thus producing data for a matched pair experiment, as shown below.
Pair
Female
Male
Differences
1
2
40.03 75.62
84.51 80.06
-44.48 -4.44
For the differences,
D
3
53.38
102.30
-48.92
x -31.1325 and
4
62.27
88.96
-26.69
D
s 20.2219.
Assume the population of differences is approximately normal. At 5% level of significance, do the data provide
sufficient evidence to indicate the mean pulling force of female firefighters is less than male firefighters?
32. We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our
sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola
of each brand. The data are shown in the following table:
Price
If the data above was collected thorough a paired difference experiment, what assumptions are needed to make
valid inferences about the mean difference of cola prices?
33. The newspaper recently ran an article indicating differences in perception of sexual harassment on the job
between men and women. The article claimed that women perceived the problem to be much more prevalent than
did the men. One question asked of both men and women was "Do you think sexual harassment is a major
problem in the American workplace?" 24% of the men and 62% of the women responded "Yes." The newspaper
created a 99.2% confidence interval for the true difference in proportions and reported it to be -.28 to -.48. What
can be said about the proportions with 99.2% reliability?
34. A sociologist wants to determine whether the proportion of women who favor the death penalty differs from the
proportion of men who favor the death penalty. He will randomly select 100 men and 125 women. Each person will
be asked whether he/she favors the death penalty.
a. Independent samples z-test
b. Independent samples t-test
c. Test for two proportions
e. Matched pairs t-test
35. A gambler has developed two strategies for betting in the game of blackjack. To test these strategies, he
decides to go gambling on a casino boat. He plays five sessions of blackjack with each strategy, with each
session consisting of 20 hands. He then records the profits of each session. Please note that a negative profit
indicates a loss. The computer output used in this analysis is shown below. The goal of the gambler is to
determine, if possible, which of the two betting strategies will result in a higher mean profit.
Ho: μ1 - μ2 > 0
versus Ha: μ1 - μ2 < 0