Mathematics, 24.01.2020 02:31 Jennifer16253

according to statistics reported on cnbc, a surprising number of motor vehicles are not covered by insurance (cnbc, february 23, 2006). sample results, consistent with the cbnc report, showed 46 out of 200 vehicles were not covered by insurance. develop a 95% confidence interval for the population proportion.

Answers: 1

Show answers

Answers

Answer from: kristalmakhija

$0.23 - 1.96\sqrt{\frac{0.23(1-0.23)}{200}}=0.172$

$0.23 + 1.96\sqrt{\frac{0.23(1-0.23)}{200}}=0.288$

The 95% confidence interval would be given by (0.172;0.288)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

X=46 number of vehicles that were not covered by insurance

n=200 random sample taken

$\hat p=\frac{46}{200}=0.23$ estimated proportion of vehicles that were not covered by insurance

true population proportion of vehicles that were not covered by insurance

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.23 - 1.96\sqrt{\frac{0.23(1-0.23)}{200}}=0.172$

$0.23 + 1.96\sqrt{\frac{0.23(1-0.23)}{200}}=0.288$

The 95% confidence interval would be given by (0.172;0.288)

Answer from: Quest

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[ (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Hurry and answer this! circle x with a radius of 6 units and circle y with a radius of 2 units are shown which steps would prove the circles similar? translate the circles so they share a common center point, and dilate circle y by a scale factor of 4. translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle y by a scale factor of 4. translate the circles so they share a common center point, and dilate circle y by a scale factor of 3. translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle y by a scale factor of 3

Answers: 1

Answer

Mathematics, 21.06.2019 16:50

Which is a true statement about an exterior angle of a triangle a. it is formed by two segments that are not sides of the triangle, b. it forms a linear pair with one of the interior angles of the triangle, c. it is complementary to one of the interior angles of the triangle. d. it is formed by two segments that are sides of the triangle.

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

How do businesses a country's economy? a. by investing in goods and services b. by increasing the unemployment rate c. by making profits

Answers: 2

Answer

Mathematics, 21.06.2019 17:30

1mile equals approximately 1.6 kilometers. which best approximates the number of miles in 6 kilometers?

Answers: 1

Answer

You know the right answer?

according to statistics reported on cnbc, a surprising number of motor vehicles are not covered by i...