Question

According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed of vehicles were not covered by insurance.

Required:
a. What is the point estimate of the proportion of vehicles not covered by insurance?
b. Develop a 95%95% confidence interval for the population proportion

Answer 1

Answer:

a) The point estimate of the proportion is the sample proportion p=0.23.

b) The 95% confidence interval for the population proportion is (0.17, 0.29).

Step-by-step explanation:

The question is incomplete:

"According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance."

a) The point estimate of the proportion is the sample proportion and is calculated as:

$\hat p=\dfrac{X}{n}=\dfrac{46}{200}=0.23$

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.23.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.23*0.77}{200}}\\\\\\ \sigma_p=\sqrt{0.000886}=0.03$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.03=0.06$

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

$LL=p-z \cdot \sigma_p = 0.23-0.06=0.17\\\\UL=p+z \cdot \sigma_p = 0.23+0.06=0.29$

The 95% confidence interval for the population proportion is (0.17, 0.29).