Crash testing evaluates the ability of an automobile to withstand a serious accident. A simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them, 8 were totaled, meaning that the cost of repairs is greater than the value of the car. Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled. Find a 95% confidence interval for the difference in the proportions of small cars and large cars that were totaled.

The  95% confidence interval for the difference between proportions is (-0.046, 0.713).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (small cars), of size n1=12 has a proportion of p1=0.6667.

The sample 2, of size n2=15 has a proportion of p2=0.3333.

The difference between proportions is (p1-p2)=0.3333.

The pooled proportion, needed to calculate the standard error, is:

The estimated standard error of the difference between means is computed using the formula:

Then, the margin of error is:

Then, the lower and upper bounds of the confidence interval are:

The  95% confidence interval for the difference between proportions is (-0.046, 0.713).

21.4 i did it already for s1

step-by-step explanation:

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