Chapter Nine
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Problem 1)
A skeptical paranormal researcher claims that the proportion
of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative
hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders
spend watching television each week is 18.4 hours. The principal introduces a campaign to
encourage the students to watch less television. One year later, the principal wants to
perform a hypothesis test to determine whether the average amount of time spent
watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance
level. What is the P-value required to
reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance
level. What is the right tail
percentile required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II
error? Provide an example of both.
Chapter 10
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Problem 1)
Steven collected data from 20 college students on their
emotional responses to classical music.
Students listened to two 30-second segments from “The Collection from
the Best of Classical Music.” After
listening to a segment, the students rated it on a scale from 1 to 10, with 1
indicating that it “made them very sad” to 10 indicating that it “made them
very happy.” Steve computes the total scores from each student and created a
variable called “hapsad.” Steve then
conducts a one-sample t-test on the data, knowing that there is an established
mean for the publication of others that have taken this test of 6. The following is the scores:
5.0 5.0
10.0 3.0
13.0 13.0
7.0 5.0
5.0 15.0
14.0 18.0
8.0 12.0
10.0 7.0
3.0 15.0
4.0 3.0
Conduct
a one-sample t-test. What is the t-test
score? What is the mean? Was the test significant? If it was significant at what P-value level
was it significant?What
is your null and alternative hypothesis? Given the results did you reject or
fail to reject the null and why?
(Use instructions on page 437 of
your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS
or Excel analysis).
Problem 2)
Billie wishes to test the hypothesis that overweight
individuals tend to eat faster than normal-weight individuals. To test this hypothesis, she has two
assistants sit in a McDonald’s restaurant and identify individuals who order
the Big Mac special for lunch. The Big
Mackers as they become known are then classified by the assistants as
overweight, normal weight, or neither overweight nor normal weight. The assistants identify 10 overweight and 10
normal weight Big Mackers. The
assistants record the amount of time it takes them to eight the Big Mac
special.
1.0 585.0
1.0 540.0
1.0 660.0
1.0 571.0
1.0 584.0
1.0 653.0
1.0 574.0
1.0 569.0
1.0 619.0
1.0 535.0
2.0 697.0
2.0 782.0
2.0 587.0
2.0 675.0
2.0 635.0
2.0 672.0
2.0 606.0
2.0 789.0
2.0 806.0
600.0
Compute
an independent-samples t-test on these data.
Report the t-value and the p values.
Where the results significant?
(Do the same thing you did for the t-test above, only this type when you
go to compare means, click on independent samples t-test. When you enter group variable into grouping
variable area, it will ask you to define the variables. Click define groups and place the number 1
into 1 and the number 2 into 2).What
is the difference between the mean of the two groups? What is the difference is standard deviation?What
is the null and alternative hypothesis?
Do the data results lead you to reject or fail to reject the null
hypothesis? What
do the results tell you?
Problem 3)
Lilly collects data on a sample of 40 high school students
to evaluate whether the proportion of female high school students who take
advanced math courses in high school varies depending upon whether they have
been raised primarily by their father or by both their mother and their
father. Two variables are found below in
the data file: math (0 = no advanced math and 1 = some advanced math) and
Parent (1= primarily father and 2 = father and mother).
Parent Math
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
2.0 0.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
Conduct
a crosstabs analysis to examine the proportion of female high school students
who take advanced math courses is different for different levels of the parent
variable.What
percent female students took advanced math classWhat
percent of female students did not take advanced math class when females were
raised by just their father?What
are the Chi-square results? What are the
expected and the observed results that were found? Are they results of the Chi-Square
significant? What do the results
mean? What
were your null and alternative hypotheses?
Did the results lead you to reject or fail to reject the null and
why?
Problem 4)
This problem will introduce the learner into a technique called
Analysis of Variance. For this course we
will only conduct a simple One-Way ANOVA and touch briefly on the important
elements of this technique. The One-Way
ANOVA is an extension of the independent –t test that can only look at two
independent sample means. We can use the
One-Way ANOVA to look at three or more independent sample means. Use the following data to conduct a One-Way
ANOVA:
Scores Group
1 1
2 1
3 1
2 2
3 2
4 2
4 3
5 3
6 3
Notice the group (grouping) variable, which is the independent
variable or factor is made up of three different groups. The scores are the dependent variable.
Use the instructions for conduction an ANOVA on page 438 of
the text for SPSS or Excel.
What
is the F-score; Are the results significant, and if so, at what level
(P-value)?If
the results are significant to the following:
Click analyze, then click Compare Means, and then select one-way ANOVA
like you did previously. Now click Post
Hoc. In this area check Tukey. If there is a significant result, we really
do not know where it is. Is it between
group 1 and 2, 1 and 3, or 2 and 3? Post
hoc tests let us isolate where the level of significance was. So if the results come back significant,
conduct the post hoc test as I mentioned above and explain where the results
were significant.What
do the results obtained from the test mean?
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