Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n = 300 accident reports from the police department. The motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are younger than age 20; 28% are 20 to 29 years old; and 56% are age 30 or older. The number of accident reports for each age group is as follows:
|Under Age||Age||Age 30 or|
a. Do the data indicate that the distribution of accidents for the three age groups is significantly different from the distribution of drivers? Test with α = .05.
b. Compute Cohen's w to measure the size of the effect.
c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.
To check: Whether the distribution of accidents (for the 3 age groups) significantly different from the distribution of drivers.
A sample of 300 accidents reports were obtained from the state department which suggested the following percentage of registered drivers age (3categories):16% are younger than 20 yrs., 28% are between 20-29 yrs. and 56% are older than 30 and up. Use to test the claim.
Step 1: Null Hypothesis and Alternate Hypothesis are:
Distribution of accidents (for the 3 age groups) is not significantly different from the distribution of drivers.
Distribution of accidents (for the 3 age groups) is significantly different from the distribution of drivers.
Step 2: For the given sample, degrees of freedom equals:
With and , the critical value (CV) is obtained from the as
Step 3: is calculated as:
The proportion of age distribution is: 0.16, 0.28 and 0.56 respectively.
The formula to calculate expected frequency is:
Substitute in the above formula and compute respective values of expected frequencies for the ages as:
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