Question

A large car insurance company is conducting a study of accidents for male and female drivers. They want to know if on average male drivers (who tend to be thought of as more aggressive drivers) have more accidents than female drivers. Data on the number of accidents in the past 5 years is collected for randomly selected drivers who are insured by this company. An analysis of the results produced the following summary statistics.

Group Statistics
                                        

	N	Mean	Std Deviation	Std Error Mean
Male	32	2.19	1.71	0.3026
Female	31	1.23	1.38	0.2482

Using α=0.01, do a complete hypothesis test and a confidence interval for this problem showing all appropriate steps and calculations. Steps that are the same for both the hypothesis test and confidence interval need not be repeated.

Answer 1

Let sampe 1: Male, sample 2: Female

Let us first check whether we can assume that population variances are equal.

F test:

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Since we can assume that population variances are equal so pooled t test should be used.

Conclusion: There is evidence to conclude that on average male drivers (who tend to be thought of as more aggressive drivers) have more accidents than female drivers.

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Here test is right tailed so we need one sided confidence interval. Let us first find the 98% confidence interval.

Since test is right tailed so corresponding one sided 99% confidence interval is (0.0228, infinity).

Since confidence interval does not contain zero so we reject the null hypothesis on the basis of confidence interval.