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Answer:
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).