I need help!!

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

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

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

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

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

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

7 0

3 years ago

Write the equation of a line in point slope form that is PARALLEL 5x + 2y = 1 that passes through the point (- 2, - 3) .

aliya0001 [1]

Answer:

y = -5/2x - 13

Step-by-step explanation:

First, we have to find the slope of the original equation

Subtract 5x from both sides

5x + 2y = 1

- 5x - 5x

2y = -5x + 1

Divide both sides by 2

2y/2 = (-5x + 1)/2

y = -5/2x + 1/2

The slope of this equation is -5/2, so -5/2 has to be in our new parallel equation

y = -5/2x + b

Plug in the given x and y

-3 = -5/2(-2) + b

-3 = 10 + b

Subtract 10 from both sides

-3 = 10 + b

- 10 - 10

b = -13

This makes our equation: y = -5/2x - 13

7 0

3 years ago

Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the n

-Dominant- [34]

Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

$A=P(1+r)^t$

Plugging values in formula, we get

$329.49=300(1+r)^2$

$\mathrm{Divide\:both\:sides\:by\:}300$

$\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}$

$\left(1+r\right)^2=1.0983$

Taking square root on both sides, we get

$1+r=\sqrt{1.0983}$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+r-1=\sqrt{1.0983}-1$

$r=\sqrt{1.0983}-1$

$r=1.048-1$

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

5 0

3 years ago

Jack is 13 years younger than his older brother, Tyler. Their Dad is twice Tyler's age. The sum of their ages now is 91. Find Ja

grin007 [14]

Answer:

13 years old

Step-by-step explanation:

So to solve this we use a system of equations. Let's use "j" to represent Jack, "t" to represent Tyler, and "d" to represent the dad. Set the system up and it will look something like this:

j = t - 13 (Jack is 13 years younger than Tyler)

d = 2t (Dad is twice Tyler's age)

d + j + t = 91 (The sum of the ages is 91)

And then solve, I solved by isolating the "j" variable on the last equation, giving us j = 91 - t - d, then plugged that into the first equation, giving us 91 - t - d = t - 13, and got d = 104 - 2t. Then I plug that into d = 2t, giving us 104 - 2t = 2t, and solve for t. T is 26, meaning Tyler is 26 years old, and then I just subtract 13 from that, giving us 13 years old.

And finally, I obviously checked my answer, because now we know dad is 52, and I got 91.

5 0

3 years ago

1/10 Florida land area of 1700000km2 Alaska

Agata [3.3K]

$1,700,000\times \frac{1}{10} = \frac{1,700,000}{10} = 170,000$

<span>Florida has a land area of 170,000 km^2</span>

4 0

3 years ago