Question

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of ten for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. At the 0.05 significance level, can we conclude that there is a difference in the mean pressures between compact, midsize or full size cars.) (Enter all numeric values in 4 decimals unless otherwise noted.)

Compact	Midsize	Fullsize
300	404	499
354	443	426
234	421	329
399	418	421
278	499	426
358	374	414
379	362	332
356	305	360
196	375	394
156	438	537

Collect the sample data and calculate the value of the test statistic

Test statistic:_______

p-value: is 0.00157

Calculate the 95% Tukey simultaneous confidence intervals. (4 decimals)

____≤μ_c-μ_m≤_____

_____≤μ_c-μ_f≤_____

_____≤μ_m-μ_f≤_____

Answer 1

87.7289 ≤μ_c-μ_m≤ 64.5289

97.8289≤μ_c-μ_f≤54.4289

86.2289≤μ_m-μ_f≤66.0289

Below are the calculations,

Tukey-Kramer Multiple Comparisons		Fromules
Mean Group 1	124.65
n Group 1	10
Mean Group 2	113.05
n Group 2	10
Mean Group 3	102.95
n Group 3	10
MSW	0.9211
Q Statistic	3.77
Comparison of Group 1 to Group 2
Absolute Difference	11.6	ABS(B3-B5)
Standard Error of Difference	0.303496293	SQRT((B9/2)*((1/B4)+(1/B6)))
Critical Range	1.144181025	B10*B13
Means of Groups 1 and 2 are	Different	IF(B12>B14,"Different","Not Different")
Comparison of Group 1 to Group 3
Absolute Difference	21.7
Standard Error of Difference	0.303496293
Critical Range	1.144181025
Means of Groups 1 and 3 are	Different
Comparison of Group 2 to Group 3
Absolute Difference	10.1
Standard Error of Difference	0.303496293
Critical Range	1.144181025
Means of Groups 2 and 3 are	Different
Group 1 vs Group 2: Diff=-11.6000, 95%CI=-87.7289 to 64.5289, p=0.9246
Group 1 vs Group 3: Diff=-21.7000, 95%CI=-97.8289 to 54.4289, p=0.7616
Group 2 vs Group 3: Diff=-10.1000, 95%CI=-86.2289 to 66.0289, p=0.9422