# 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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