Question

Below are matched pair data consisting of driving test scores for a sample of 11 licensed drivers before and after they took an online traffic safety class. At a 0.05 significance level, use the sign test to test the claim that taking this online class affects driving test scores.

Before	31	44	40	50	53	48	59	31	38	58	55
After	31	47	41	48	52	52	55	35	37	59	55

(a) What is the value of the test statistic used in this sign test?

(b) What is the critical value in this sign test?

(c) What is the correct conclusion of this sign test?

• There is not sufficient evidence to support the claim that the online class affects driving test scores.
• There is sufficient evidence to warrant rejection of the claim that the online class affects driving test scores.
• There is not sufficient evidence to warrant rejection of the claim that the online class affects driving test scores.
• There is sufficient evidence to support the claim that the online class affects driving test scores.

Answer 1

Answer:

provided information

Null and Alternative Hypotheses:

Ho: Median of Differences = 0

Ha: Median of Differences > 0

a)test statistics:

Differences between( Before-After)

0
-3
-1
2
1
-4
4
-4
1
-1
0

Positive sign count (x⁺)= 4
Negative sign count(x^-) = 5
Total count = 9

The test statistic is X = min{X⁺, X^-}

X= min{4, 5}= 4

b)critical value:

The critical value for the signficance level provided and the type of tail is X* = 1

(c) Decision rule:

Accepted H_o, because X>X^*

There is not sufficient evidence to support claim that the online class affects driving test scores.

Thank you!

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