4) The National Transportation

4) The National Transportation Safety Board (NTSB) wanted toexamine the safety of three different car types, as measured byhead crash test percentages. Cars were classified into threegroups: compact (M = , SS = ), midsized (M = , SS = ), andfull-size (M = , SS = ). A one-way ANOVA was conducted anddetermine that there was a statistically significant (or nosignificant) difference between safety and type of car, F( ___,_____) = _________.


To examine the safety of three different car types, as measuredby head crash test percentages data example:

Compact Cars MidSize Cars Full Size Cars
541 350 380
530 333 353
604 510 303

Now state the null and alternative hypothesis:

The significance level = 0.05.

Find Mean(M) and Sum of Square(SS):

From above calculation Mean(M) and Sum of Square(SS) forthree groups:

For Compact Cars:

M = 558.333 and SS = 3188.66

For MidSize Cars:

M = 397.667 and SS = 19072.66

For Full Size Cars:

M = 345.333 and SS = 3052.66

Now Find F statistics:

The total size is 9

The size in each group is 3.

Degree of freedom of within gruops.

Take Grand total of each value.

Take the total of each group then sum of the square.

SS between = SS total – SS within = 99235.556 – 25314 =73921.556

F critical value with degree of freedom (2,6) at 0.05 =5.143

So, F- statistics is greater than F critical value, we rejectthe null hypothesis, so there is a significant difference.

APA format:

compact (M = 558.333, SS = 3188.66), midsized (M = 397.667, SS =19072.66 ), and full-size (M = 345.333, SS = 3052.66). A one-wayANOVA was conducted and determine that there was a statisticallysignificant difference between safety and type of car, F( 2, 6) =8.761.

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