4a . The researcher wants to use this data to determine if the stopping distance

Question

4a. The researcher wants to use this data to determine if the stopping distance on wet pavement is greater than the stopping distance on dry pavement. The researchers used a paired research design as shown in the data set above. Explain why this format is a called a paired design.

4b. State the null and alternative hypothesis for this test. Define the parameter of interest.

4c.

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Wet Pavement and Dry Pavement
H0 : D = 0
HA : D 0
Hypothesis test results:

Difference

Mean

Std. Err.

DF

T-Stat

P-value

Wet Pavement - Dry Pavement

63.3

5.4813826

9

11.548181

<0.0001

Differences stored in column, Differences.

4d. As the researcher used a very small sample size we must verify that the distribution of differences is Normally distributed. Use your boxplot to verify that this condition has been satisfied.

4e. Make a decision concerning your hypothesis test using a significance level of 0.05.

4f. State your conclusion in the context of the question.

Difference

Mean

Std. Err.

DF

T-Stat

P-value

Wet Pavement - Dry Pavement

63.3

5.4813826

9

11.548181

<0.0001

Explanation / Answer

Question 4a

This format is called as a paired design because the data is bivariate in nature and it is related data. We have the data for the same pavement with wet and dry.

Question 4b

Null Hypothesis: H0: The stopping distance on wet pavement is same as the stopping distance on dry pavement.

Alternative hypothesis: Ha: The stopping distance on wet pavement is greater than the stopping distance on dry pavement.

Parameter of interest is mean of the difference between Wet Pavement and Dry Pavement

Question 4c

The hypothesis test results indicate that p-value is very less and we would reject the null hypothesis.

Question 4e

For the given paired t test, we get the p-value less than 0.0001 which is very less than given level of significance or alpha value 0.05, so we reject the null hypothesis.

Question 4f

We reject the null hypothesis that stopping distance on wet pavement is same as the stopping distance on dry pavement. This means there is sufficient evidence to conclude that the stopping distance on wet pavement is greater than the stopping distance on dry pavement.

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