8A MC

Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets?  A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse.  He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state.  Conduct a significance test that would help answer the columnist’s question.

What is the appropriate null hypothesis?

• The observed counts are all equal to 30.

• The observed number of speeding tickets is the same for all four color groups.

• At least one of the four car color percentages is different from the other three.

• The distribution of car colors for the speeding citations is the same as the distribution of colors for all cars on the highway in this state.

• The observed counts are equal to the expected counts.

Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets?  A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse.  He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state.  Conduct a significance test that would help answer the columnist’s question.

What are the expected counts?

• red: 16   white/silver: 33   gray/black: 39   other: 32

• red: 16.8   white/silver: 42.0   gray/black: 27.6   other: 33.6

• red: 14   white/silver: 35   gray/black: 23   other: 28

• red: 13.3   white/silver: 27.5   gray/black: 32.5   other: 26.7

• red: 30   white/silver: 30   gray/black: 30   other: 30

Tags

CCSS.HSS.MD.A.2

The chi-square test statistic is 6.75, which yields a P-value of 0.08.  Which is an appropriate conclusion to draw?

• Accept H₀ at the α=005 level.  There is little evidence that certain car colors get more speeding tickets than others.   

• Accept H_a at the α=0.01 level.  There is evidence that certain car colors get more speeding tickets than others. 

• Accept H_a at the α=0.01 level.  We do not have sufficient evidence to conclude that certain car colors get more speeding tickets than others.   

• Fail to reject H₀ at the α=0.01 level.  We do not have sufficient evidence to conclude that certain car colors get more speeding tickets than others. 

• Reject H₀ at the α=0.05 level.  There is evidence that certain car colors get more speeding tickets than others. 

For this test, we should use the χ² distribution with ____ degrees of freedom.

• 3

• 4

• 30

• 119

• 120

Which statement is true about chi-square distributions? 

• As the number of degrees of freedom increases, the distribution looks less like a normal curve.

• As the number of degrees of freedom increases, the distribution looks more like a uniform distribution.

• Their density curves are skewed to the left.

• They take on only positive values. 

• All of these choices are true.

Which is a condition that must be satisfied in order to use a chi-square goodness-of-fit test? 

• The expected count for each category is greater than 5. 

• The sample size is greater than 30. 

• The expected count is the same for each category.

• The number of categories is small relative to the number of observations.

• The population distribution is approximately Normal.