Worksheet for Lesson 3_Part 2 (or Output 4)
Directions: Identify the most appropriate statistical test given the following research
problems/situations. In each case, give a brief explanation.
1. The expenditures per pupil in three provinces of the country are listed. Using a 0.05
level of significance, can you conclude that there is a difference in means?
Province A
Province B
Province C
4946
6149
7451
8605 6202
7243
6479
5282
5953
6000
6528
6911
6113
2. Adults aged 16 or older were assessed in three types of literacy in 2003: prose,
document, and quantitative. The scores in document literacy were the same for 19to 24-year-olds and for 40- to 49-year-olds. A random sample of scores from a later
year showed the following statistics. At 0.05 level of significance, can a difference
between age groups be concluded?
3. An obstacle course was set up on a campus, and 10 volunteers were given a chance
to complete it while they were being timed. They then sampled a new energy drink
and were given the opportunity to run the course again. The “before” and “after”
times in seconds are shown below. Is there sufficient evidence at a 0.05 level to
conclude that the students did better the second time?
4. The average family size was reported as 3.18. A random sample of families in a
particular school district resulted in the following family sizes. At a 0.05, does the
average family size differ from the national average?
5. A survey taken several years ago found that the average time a person spent reading
the local daily newspaper was 10.8 minutes. The standard deviation of the
population was 3 minutes. To see whether the average time had changed since the
newspaper’s format was revised, the newspaper editor surveyed 36 individuals. The
average time that the 36 people spent reading the paper was 12.2 minutes. At 0.05,
is there a change in the average time an individual spends reading the newspaper?
6. According to Nielsen Media Research, children (ages 2–11) spend an average of 21
hours 30 minutes watching television per week while teens (ages 12–17) spend an
average of 20 hours 40 minutes. Based on the sample statistics obtained below, is
there sufficient evidence to conclude a difference in average television watching
times between the two groups? Use 0.01 level of significance.
7. A survey found that 83% of the men questioned preferred computer-assisted
instruction to lecture and 75% of the women preferred computer-assisted
instruction to lecture. There were 100 individuals in each sample. At 0.05 level, test
the claim that there is no difference in the proportion of men and the proportion of
women who favor computer-assisted instruction over lecture.
8. The percentages of adults 25 years of age and older who have completed 4 or more
years of college are 23.6% for females and 27.8% for males. A random sample of
women and men who were 25 years old or older was surveyed with these results. At
0.01 level, can it be concluded that there is a difference between these groups?
9. A survey of 800 recent degree recipients found that 155 received associate degrees;
450, bachelor degrees; 20, first professional degrees; 160, master degrees; and 15,
doctorates. Is there sufficient evidence to conclude that at least one of the
proportions differs from a report which stated that 23.3% were associate degrees;
51.1%, bachelor degrees; 3%, first professional degrees; 20.6%, master degrees; and
2%, doctorates? Use 0.05 level of significance.
10. The table below shows the number of students (in thousands) participating in
various programs at both two-year and four-year institutions. At 0.05 level, can it be
concluded that there is a relationship between program of study and type of
institution?
11. A statistics instructor wanted to see if student participation in review preparation
methods led to higher examination scores. Five students were randomly selected
and placed in each test group for a three-week unit on statistical inference. Everyone
took the same examination at the end of the unit, and the resulting scores are
shown below. Is there sufficient evidence at 0.05 level to conclude an interaction
between the two factors? Is there sufficient evidence to conclude a difference in
mean scores based on formula delivery system? Is there sufficient evidence to
conclude a difference in mean scores based on the review organization technique?
12. The number of faculty and the number of students are shown for a random selection
of small colleges. At 0.05 level, is there a significant relationship between the two
variables?
13. A study claims that all adults spend an average of 14 hours or more on chores during
a weekend. A researcher wanted to check if this claim is true. A random sample of
200 adults taken by this researcher showed that these adults spend an average of
14.65 hours on chores during a weekend. The population standard deviation is
known to be 3.0 hours. At 0.05 level, is the claim true?
14. The president of a university claims that the mean time spent partying by all
students at this university is not more than 7 hours per week. A random sample of
40 students taken from this university showed that they spent an average of 9.50
hours partying the previous week with a standard deviation of 2.3 hours. Test at the
0.05 significance level whether the president’s claim is true.
15. Many students graduate from college deeply in debt from student loans, credit card
debts, and so on. A sociologist took a random sample of 401 single persons, classified
them by gender, and asked, “Would you consider marrying someone who was Php
2,500,000 or more in debt?” The results of this survey are shown in the following
table. Test at the 1% significance level whether gender and response are related.
16. The data given in the table below are the midterm scores in a course for a sample of
10 students and the scores of student evaluations of the instructor. (In the instructor
evaluation scores, 1 is the lowest and 4 is the highest score.)Predict the midterm
score in terms of the instructor score.
17. A university employment office wants to compare the time taken by graduates with
three different majors to find their first full-time job after graduation. The following
table lists the time (in days) taken to find their first full-time job after graduation for
a random sample of eight business majors, seven computer science majors, and six
engineering majors who graduated in May 2020. At the 5% significance level, can
you conclude that the mean time taken to find their first full-time job for all May
2020 graduates in these fields is the same?
18. In a sample of 50 men, 44 said that they had less leisure time today than they had 10
years ago. In a sample of 50 women, 48 women said that they had less leisure time
than they had 10 years ago. At 0.05 level, is there a difference in the proportions?
19. According to Nielsen Media Research, children (ages 2–11) spend an average of 21
hours 30 minutes watching television per week while teens (ages 12–17) spend an
average of 20 hours 40 minutes. Based on the sample statistics obtained below, is
there sufficient evidence to conclude a difference in average television watching
times between the two groups? Use 0.01 level of significance.
20. This table lists the numbers of officers and enlisted personnel for women in the
military. At 0.05 level, is there sufficient evidence to conclude that a relationship
exists between rank and branch of the Armed Forces?