The National Highway Traffic Safety Administration NHTSA per

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.

Solution

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