Question

In: Statistics and Probability

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize...

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≤_____

Solutions

Expert Solution

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

orchestra answered 3 years ago
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