Question

In: Statistics and Probability

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

Suppose the National Transportation Safety Board wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Test the claim that the mean pressure applied to the driver's head during a crash is equal for all three types of cars. Use α = 0.05

Compact Cars 643 655 702
Midsize Cars 469 427 525
Full-size Cars 484 456 402

Show your 6 steps labeled in order in the box below.

Solutions

Expert Solution

count, ni = 3 3 3
mean , x̅ i = 666.667 473.67 447.33
std. dev., si = 31.182 49.166 41.681
sample variances, si^2 = 972.333 2417.333 1737.333
total sum 2000 1421 1342 4763 (grand sum)
grand mean , x̅̅ = Σni*x̅i/Σni =   529.22
square of deviation of sample mean from grand mean,( x̅ - x̅̅)² 18890.975 3086.420 6705.790
TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² = 56672.926 9259.259 20117.370 86049.55556
SS(within ) = SSW = Σ(n-1)s² = 1944.667 4834.667 3474.667 10254.0000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   9
df within = N-k =   6
  
mean square between groups , MSB = SSB/k-1 =    43024.7778
  
mean square within groups , MSW = SSW/N-k =    1709.0000
  
F-stat = MSB/MSW =    25.1754
P value =   0.0012

SS df MS F p-value F-critical
Between: 86049.56 2 43024.78 25.18 0.0012 5.14
Within: 10254.00 6 1709.00
Total: 96303.56 8
α = 0.05
conclusion : p-value<α , reject null hypothesis    

Not all means are equal.

THANKS

revert back for doubt

please upvote


Related Solutions

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...
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 cars each of the cars types. The data below displays the frontal crash test performance percentages. Test whether there are statistical differences in the frontal crash test performance for each type of car. Compact Cars Midsize Cars Full-Size Cars 95 95 93 98 98 97 87 98 92 99 89 92 99 94 84 94...
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 three for each of the treatments (cars types). Using the 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. Use α = 5%. Compact cars Midsize cars Full-size cars 64 46 47 65 43 45 69 52 40 Average: 66...
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 three for each of the car types. Using the data provided below Pressure Car Type 643 Compact 655 Compact 702 Compact 469 MidSize 427 MidSize 525 MidSize 484 FullSize 456 FullSize 402 FullSize Test, using Mood’s Median Test, whether the median pressure applied to the driver’s head during a crash test is equal for each...
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 cars each of the cars types. The data below displays the frontal crash test performance percentages. Compact Cars Midsize Cars Full-Size Cars 95 95 93 98 98 97 87 98 92 99 89 92 99 94 84 94 88 87 99 93 88 98 99 89 Patrick wants to purchase a new car, but he...
7. Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars,...
7. 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 three for each of the treatments (cars types). The hypothetical data provided below from 10 trials report the mean pressure applied to the driver’s head during a crash test for each type of car. Compact: 635, 671, 648, 685, 648, 651, 654, 682, 687, 627 Midsize: 482, 529, 541, 518, 497, 526, 507, 492,...
– Analysis of Variance Suppose we want to examine the safety of compact cars, midsize cars,...
– Analysis of Variance Suppose we want to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of five for each type of cars. Test, whether the mean pressure applied to the driver’s head during a crash test, is equal for each types of car and tell which type of cars had a significant effect on the accident injuries. Use α = 5%. Compact cars midsize cars full-size cars 625 437 490 675 475...
4) The National Transportation Safety Board (NTSB) wanted to examine the safety of three different car...
4) The National Transportation Safety Board (NTSB) wanted to examine the safety of three different car types, as measured by head crash test percentages. Cars were classified into three groups: compact (M = , SS = ), midsized (M = , SS = ), and full-size (M = , SS = ). A one-way ANOVA was conducted and determine that there was a statistically significant (or no significant) difference between safety and type of car, F( ___, _____) = _________.
The Ontario Ministry of Transportation is studying the relative safety of compact cars, mid-sized cars, and...
The Ontario Ministry of Transportation is studying the relative safety of compact cars, mid-sized cars, and full size cars. Safety data is collected from a random sample of four cars for each of three car types. Using the data provided below, test whether the mean pressure applied to the driver’s head during a crash test is on average equal for each of the car types. Use a significance level of 1%. Please show all the steps Compact Mid-Sized Full Sized...
A business consultant for the National Transportation Safety Board (NTSB), collected data on the safety of...
A business consultant for the National Transportation Safety Board (NTSB), collected data on the safety of hybrid automobiles traveling at 30, 40 and 50 miles per hour.  She randomly assigned the same hybrid model to each condition and collected data on the pressure applied to the driver’s head during a crash into a wall at each speed. What is the independent variable? Dependent variable? Is she able to make cause and effect statements about the cars the head pressure? Explain. ...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT