Stats 250 W12 Exam 2 Solutions
1. Age at first marriage
–
A researcher investigating changing trends in marriage wants to determine if the
average age of first marriage is higher for men than for women.
He takes a random sample of 30 recently
married heterosexual couples from a list of newspaper wedding announcements and records the ages of
the man and woman for each couple.
An excerpt of the data is shown below:
Couple
Male age
Female age
Difference (M
1
27.3
27.6
-0.3
2
28.5
27.8
…
30
30.7
32.4
-1.7
Mean
28.2
27.6
0.65
Standard Deviation
2.8
3.2
a. State the appropriate hypotheses to test the researcher's theory and complete the definition of the
corresponding parameter.
The research has decided to use a 5% significance level.
–
F)
0.7
1.5
[3]
H
0
: ____
d
= 0
_________________
H
a
: ________
d
> 0
_____________________
where the parameter represents
the population mean difference ___
in age at first marriage (m
–
f) for all couples
________
b.
Use the SPSS output to complete the statement by filling in the blank and circling the appropriate word:
[2]
The observed sample mean difference in ages is ____
2.37
________ standard errors
(Circle one)
ABOVE
BELOW
the hypothesized population mean difference in ages.
c.
If there really is no difference in the average age of first marriage for men and women in the population of
all such couples, what is the expected value of the test statistic?
[1]
Final answer _______
0
_______
d.
Provide a complete sketch of the
p
-value;
include a label and values on the x axis, a full
label for the distribution, the shaded area for
the
p
-value, and the actual value of the
p
-value
[4]
p
-value = ____
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std.
Deviation
Std. Error
Mean
95% Confidence Interval of the
Difference
Lower
Upper
Pair 1
m - f
.65
1.50
.2746
.09
1.21
2.37
29
.024

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[1]
f.
What type of error could the researcher have made?
[1]
(circle one)
Type I Error
Type II Error
Cannot be determined

e.
0

Stats 250 W12 Exam 2 Solutions
2.
Caffeine Consumption
–
Concerned about caffeine consumption by young adults, a doctor decides to
investigate the caffeine consumption of college students and high school students.
She randomly samples
72 college students (group 1) and 64 high school students (group 2) to investigate if the mean caffeine
consumption (in mg) differs between college students and high school students.
It has been a few years
since she took her statistics course, so she uses Google to find a few commands in SPSS and obtains the
output below:
a. The
researcher
wishes
to
estimate
the
difference
in
population
mean
caffeine
(college
–
high school) using a 95% confidence interval. She would like to use the pooled procedure.
She
notes that the two sample standard deviations are somewhat similar, but would like to be further assured
by
examining Levene’s Test results
i.
Clearly state the null hypothesis for Levene
’s Test.
consumption
.
[1]

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