The National Highway Traffic Safety Administration (NHTSA) performed a series of
ID: 3431517 • Letter: T
Question
The National Highway Traffic Safety Administration (NHTSA) performed a series of brake tests to evaluate variability in the results obtained at the different facilities and among different drivers. This table displays the braking distance in feet, from two different test sites for the Chevrolet Blazer on dry Surface. Is there statistically significant evidence that the average braking distance at the two test sites is different? Explain using the four-step process and test at the 5% level of significance. As there is no information about the design of this study, treat it as an observational study when you write the conclusion.Explanation / Answer
Null hypothesis: ?1 = ?2
Alternative hypothesis: ?1 ? ?2
Two sample t test is used
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
10
Sample Mean
159.48
Sample Standard Deviation
2.92
Population 2 Sample
Sample Size
14
Sample Mean
162.93
Sample Standard Deviation
3.92
Intermediate Calculations
Population 1 Sample Degrees of Freedom
9
Population 2 Sample Degrees of Freedom
13
Total Degrees of Freedom
22
Pooled Variance
12.5682
Standard Error
1.4678
Difference in Sample Means
-3.4500
t Test Statistic
-2.3504
Two-Tail Test
Lower Critical Value
-2.0739
Upper Critical Value
2.0739
Calculated t = -2.3504
Calculated t = -2.3504 < -2.0739, the lower critical value
This falls in the rejection region
We reject the null hypothesis
We conclude that average braking distance at the two sites are different.
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
10
Sample Mean
159.48
Sample Standard Deviation
2.92
Population 2 Sample
Sample Size
14
Sample Mean
162.93
Sample Standard Deviation
3.92
Intermediate Calculations
Population 1 Sample Degrees of Freedom
9
Population 2 Sample Degrees of Freedom
13
Total Degrees of Freedom
22
Pooled Variance
12.5682
Standard Error
1.4678
Difference in Sample Means
-3.4500
t Test Statistic
-2.3504
Two-Tail Test
Lower Critical Value
-2.0739
Upper Critical Value
2.0739
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