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# Hypothesis Testing: Paired t test

A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during a six-month period before and after the modifications are provided. At the .05 significance level, can it be concluded that the modifications reduced the number of accidents?

Before After
A 7 3
B 7 7
C 6 7
D 4 0
E 8 4
F 9 6
G 8 8
H 10 5

A. What type of test would be appropriate for this problem?
A. Z-test - single samples
B. Z-test - proportions
C. T-test of independence
D. Paired samples t-test
E. ANOVA

B.What is the hypotheses?
F. &#956;Before = &#956;After; &#956;Before &#8800; &#956;After
G. &#956;Before &#8805; &#956;After; &#956;Before < &#956;After
H. &#956;Before &#8804; &#956;After; &#956;Before > &#956;After
I. &#956;Before = &#956;After; &#956;Before < &#956;After
J. &#956;Before &#8804; &#956;After; &#956;Before &#8800; &#956;After

C. What is the test statistic?
a. -2.89
b. 2.89
c. 1.89
d. -1.89
e. .01

D. What is the critical value?
a. -2.89
b. 2.89
c. 1.89
d. -1.89
e. .01

E. What is the decision?
a. Accept the null of no difference. The modification did not have an impact on the number of accidents.
b. Accept the null of no difference. The modification did have an impact on the number of accidents.
c. Reject the null of no difference. The modification did not have an impact on the number of accidents.
d. Reject the null of no difference. The modification did have an impact on the number of accidents.
e. Cannot determine from the information provided.

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for paired t test. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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