# Confidence Interval of Difference Questions

3. A researcher was interested in understanding how the age of onset (i.e., age at which juveniles were
comparison between Hispanic and White juveniles. She performed statistical analysis of the data she
arrested for the offense the very first time) would vary by ethnicity. Specifically, she would like to make a
collected and obtained the following results.
Race and Ethnicity
White
Hispanic
Mean
16.575
15.895
N
58
44
Std. Deviation
1.500
1.446
AGE AT ARREST
Std. Error Mean
.199
.221
Levene’s Test
for Equality of
Variances
t-Test for Equality of Means
95% Confidence Interval of
the Difference
Lower Upper
0.090
1.270
Std. Error
Difference
.298
Sig. (2-
tailed)
.023
Mean
Difference
A
df
AGE AT
ARREST
F
4.626
Sig.
.042
B
D
0.098
1.262
Equal variances
assumed
Equal variances
not assumed
.294
С
A
92
.021
Using information from the above two tables, answer the following questions.
(1.5 points) What level of a has been used in this hypothesis testing? Explain how a was set and
a.
obtained from the above tables.
b. (2 points) Is the assumption of equal variances violated? Identify the p value from Levene’s test
and use it to explain why this assumption is violated or why it is not violated.
c. (1.5 points) Based on information from the above two tables, what type of t-test has been used
for this hypothesis testing? Why?
.d. (2 points) Based on the scenario, use complete sentences to state the null (Ho) and alternative
(Hi) hypotheses in a two-tailed t-test?
Ho:
Hj:
Page 3 of 4
e. (1 point) What is the mean difference in Cell A?
f. (2 points) What is the calculated t value with equal variances assumed in Cell B? What is the
calculated t value with equal variances not assumed in Cell C? Identify the formula and provide
all calculations below.
g. (1 point) Calculate the degrees of freedom with equal variances assumed in Cell D. Provide your
calculations.
h. (2 points) Which calculated t value in the second table is appropriate to be used for the current t-
test. Clearly explain the answer based on the result of Levene’s test.
i. (2.5 points) Using the calculated t value in the row you have chosen for the t-test, find the critical
t, make a comparison between the calculated t and the critical t, and draw a conclusion on the
hypothesis. Clearly explain how you reach the conclusion based on t statistics.
is to be used based on the result of Levene’s test?
j. (1 point) There are two p values under the t-test for testing the equality of means. Which p value
k. (1.5 points) Based on the p value found in the preceding question, determine whether the null
hypothesis in Question 3d is rejected. Clearly explain how you reach the conclusion based on the
p value.

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