1. A small component in an electronic device has two small holes where another tiny part is
fitted. In the manufacturing process the average distance between the two holes must be
tightly controlled at 0.02 mm, else many units would be defective and wasted. Many times,
throughout the day, quality control engineers take a small sample of the components from
the production line, measure the distance between the two holes, and make adjustments if
needed. Suppose at one time four units are taken and the distances are measured as:
0.021
0.019
0.023
0.020
Determine, at the 1% level of significance, if there is sufficient evidence in the sample to
conclude that an adjustment is needed. Assume the distances of interest are normally
distributed.
2. The price of a popular tennis racket at a national chain store is $179 Portia bought five of
the same racket at an online auction site for the following prices:
155
179
175
175
161
Assuming that the auction prices of rackets are normally distributed, determine whether
there is sufficient evidence in the sample, at the 5% level of significance, to conclude that the
average price of the racket is less than $179 if purchased at an online auction.
3. Consider our earlier example about teenagers and Internet access. According to the Kaiser
Family Foundation, 84% of U.S. children ages 8 to 18 had Internet access at home as of
August 2009. Researchers wonder if this number has changed since then. Sample consisted
of 500 children, and 86% of them had Internet access at home. Use α = 0.05
4. A concern was raised in Australia that the percentage of deaths of Aboriginal prisoners was
higher than the percent of deaths of non-Aboriginal prisoners, which is 0.27%. A sample of
six years (1990-1995) of data was collected, and it was found that out of 14,495 Aboriginal
prisoners, 51 died ("Indigenous deaths in," 1996). Do the data provide enough evidence to
show that the proportion of deaths of Aboriginal prisoners is more than 0.27%?
5. A student at a four-year college claim that mean enrollment at four–year colleges is higher
than at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–
year colleges surveyed; the mean enrollment was 5,068 with a standard deviation of 4,777.
Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard
deviation of 8,191. Use α = 0.01.
6. Mean entry-level salaries for college graduates with mechanical engineering degrees and
electrical engineering degrees are believed to be approximately the same. A recruiting office
thinks that the mean mechanical engineering salary is lower than the mean electrical
engineering salary. The recruiting office randomly surveys 50 entry level mechanical
engineers and 60 entry level electrical engineers. Their mean salaries were $46,100 and
$46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively.
Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical
engineering salary is lower than the mean entry-level electrical engineering salary.
7. A group of students conducted tutorial sessions on elementary pupils. The instructor
wanted to determine if their sessions was effective and the scores of the pupils are better
after the tutorial sessions. Here are the pupils’ scores before and after the session:
Pupils
a
b
c
d
e
Before
10
12
11
14
9
After
15
13
13
10
9
Using α = 0.1, test if tutorial sessions are effective.
8. Researchers say that vegetarian diet is an effective vegetarian diet. To test this claim, they
gathered 9 people that were willing to participate and be observed for 2 weeks. Below are
the tabulated results of their experiment.
Participants
1
2
3
4
5
6
7
8
9
Before the
70
67
66
65
60
71
65
68
72
experiment
After the
65
60
60
61
54
60
60
59
66
experiment
Test if the researchers claim is true at α = 0.15.
9. 50 out of 150 respondents from ABC Academy agreed that the extracurricular activities are
beneficial to their learning. Meanwhile, 70 out of 100 respondents from XYZ University said
otherwise. Check if there is a significant difference between the proportions at α = 0.05.
10. A recent year was randomly picked from 1985 to the present. In that year, there were 2,051
Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College,
there were 321 Hispanic students out of a total of 2,441 students. In general, do you think
that the percent of Hispanic students at the two colleges is basically the same or different?
11. A researcher claims that there is a difference in the average age of assistant professors,
associate professors, and full professors at her university. Faculty members are selected
randomly, and their ages are recorded. Assume faculty ages are normally distributed. Test
the claim at the α = 0.05 significance level. The data are listed below.
Assistant
28
32
36
42
50
33
38
Prof
Associate
44
61
52
54
62
45
46
Prof
Prof
54
56
55
65
52
50
46
12. A local college wants to compare the mean GPA for players on four of its sports teams:
basketball, baseball, hockey, and lacrosse. A random sample of players was taken from each
team and their GPA recorded in the table below.
Basketball
Baseball
Hockey
Lacrosse
3.6
2.1
4.0
2.0
2.9
2.6
2.0
3.6
2.5
3.9
2.6
3.9
3.3
3.1
3.2
2.7
3.8
3.4
3.2
2.5
Assume the populations are normally distributed and have equal variances. At the 5%
significance level, is there a difference in the average GPA between the sports team.