Numbers and letters in the alphabet - numbers of the months in the year

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

Pls asap completing square X^2 -24x+5=0

anzhelika [568]

Answer:

Step-by-step explanation:

x² - 24x + 5 = 0

x² - 24x = -5

Now divide the co efficient of x by 2 and square the quotient and add to both sides

24/2 = 12

12² = 144. Now add 144 to both sides of the equation.

x² - 24x + 144 = 5 + 144

x² - 24x + 144 = 149

x² - 2*12*x + 12² = 149

(x - 12)² = 149

Both sides take square root

x - 12 = ±√149

x = 12 ± √149

4 0

2 years ago

Betty makes pie to make 6 pies she used 7 1/2 cups of flour how many cups of flour are needed to make 1 pie

MrRissso [65]

Answer:

One and one fourth or 1 1/4 cups of flour is needed to make one pie

Step-by-step explanation:

7 1/2 divided by 6 = 1 1/4

5 0

3 years ago

Plz help Im behind.!! Asap will give brainliest if the answers right

german

Answer:

l = (P-2w)/2

Step-by-step explanation:

P = 2l + 2w

move 2w to the left to leave the l variable by itself

P - 2w = 2l

divide by 2 on both sides to leave l by itself

(P - 2w) / 2 = l or l = (P - 2w) / 2

3 0

3 years ago

Read 2 more answers

How many solutions does x2 - 2x + 9 = 0 have and what type are they? Do NOT find the

Temka [501]

Answer:

3

Step-by-step explanation:

7 0

3 years ago