Question

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( ___, _____) = _________.

Answer 1

To examine the safety of three different car types, as measured by 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) for three 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 reject the 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-way ANOVA was conducted and determine that there was a statistically significant difference between safety and type of car, F( 2, 6) = 8.761.