Question

1. A highway safety institution conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the institute’s 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver’s side. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40mph. You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles (SUV’s). The data in the tables below were collected from the institute’s study. Use α=.01.

Large Family Cars 262 135 413 526 148 630 164

Passenger Vans 149 237 341 697 554 466 319

Midsize Utility Vehicles 225 216 146 255 402 596 395

State the null and alternative hypothesis.

h_0:

h_A:

Calculate the sample standard deviation of each sample. Do we meet the requirement for these?

Find the test statistic. F_0=

Determine the P-value. p=

State your conclusion.

Would we perform post-hoc procedures for this data?

Answer 1

Using Excel, go to Data, select Data Analysis, choose Anova: Single Factor. Group by rows at alpha = 0.01

SUMMARY
Groups	Count	Sum	Average	Variance
Large Family Cars	7	2278	325.43	39747.95
Passenger Vans	7	2763	394.71	35949.57
Midsize Utility	7	2235	319.29	23810.57

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	24564.67	2	12282.33	0.37	0.70	6.01
Within Groups	597048.57	18	33169.37
Total	621613.24	20

h_0: μ₁ = μ₂ = μ₃, Mean head injury resulting from this offset crash is the same for the three cars

h_A: At least one μ_i is different, Mean head injury resulting from this offset crash is not the same for the three cars

Calculate the sample standard deviation of each sample. Do we meet the requirement for these?

Large Family Cars = 39747.95^0.5 = 199.37

Passenger Vans = 35949.57^0.5 = 189.60

Midsize Utility = 23810.57^0.5 = 154.31

Test statistic. F_0= 0.37

P-value. p = 0.696

Conclusion: Since p-value is more than 0.696, we do not reject the null hypothesis and conclude that mean head injury resulting from this offset crash is the same for the three cars.

Since μ₁ = μ₂ = μ₃, we do not perform post-hoc procedures for this data.