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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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
20 20-28 Older
68 92 140

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.

a.

To determine

To check: Whether the distribution of accidents (for the 3 age groups) significantly different from the distribution of drivers.

Explanation

Given info:

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 α=0.05 to test the claim.

Calculation:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: Distribution of accidents (for the 3 age groups) is not significantly different from the distribution of drivers.

H1: 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:

df=(C1)   where C equals number of categories=31=2

With α=0.05 and df=2, the critical value (CV)  is obtained from the χ2table as

χ2=5.991

 Step 3: χ2statistics is calculated as:

χ2=(fofe)2fe

The proportion of age distribution is: 0.16, 0.28 and 0.56 respectively.

The formula to calculate expected frequency is:

fe=p×n

Substitute n=300 in the above formula and compute respective values of expected frequencies for the ages as:

fe,20=0

c.

To determine
How would the outcome of hypothesis test will be written in the report.

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