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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

Simplify the following expressions. All answers should be in standard form.

Ratling [72]

Answer:

The given expression in simplified form is: $15x^2+10x$

Step-by-step explanation:

Simplifying the expression involve reducing the number of terms to minimum and making the expressions in standard form.

This may involve addition, subtraction and multiplication of variables.

Given expression is:

$5x(3x+2)$

Distributing 5x will give us:

$= 5.3.x.x + 5.2.x\\=15x^2+10x$

Hence,

The given expression in simplified form is: $15x^2+10x$

6 0

3 years ago

In a system of linear equations in two variables, if the graphs of the equations are the same, the equations are (blank) equat

makkiz [27]

Answer:

Please check the explanation.

Step-by-step explanation:

We know that when a consistent system has infinite solutions, then the graphs of the equations are exactly the same. In other words, these equations are called dependent equations.

All points of dependent equations share the same slope and same y-intercept.

For example,

6x-2y = 18

9x-3y=27

represent the dependent equations.

Writing both equations in slope-intercept form

y=mx+c

where m is the slope and c is the y-intercept

Now

6x-2y=18

2y = 6x-18

Divide both sides by 2

y = 3x - 9

Thus, the slope = 3 and y-intercept = b = -9

now

9x-3y=27

3y = 9x-27

Divide both sides by 3

y = 3x - 9

Thus, the slope = 3 and y-intercept = b = -9

Therefore, both equations have the same slope and y-intercept. Their graphs are the same. Hence, they are called dependent equations.

5 0

3 years ago

A rectangle on a coordinate plane has vertices Q(-1, 1), R(6,1), S(6,-8), and T(-1,-8). What are the dimensions of the rectangle

xeze [42]

Answer:

The length is 9.

The width is 7.

Step-by-step explanation:

A rectangle has two dimensions.

The width, which is the distance between the points who have the same value of y.

The length, which is the distance between the points who have the same value of x.

Distance between 2 points:

Points (a,b) and (c,d).

$D = \sqrt{(c-a)^{2} + (d-b)^{2}}$

Same value of x:

(-1,1), (-1-8) or (6,1), (6,-8)

The distance for both of them is the same, can calculate for only one.

$L = \sqrt{(6-6)^{2} + (-8 - 1)^{2}} = \sqrt{81} = 9$

The length is 9.

Same value of y:

(-1,1), (6,1) or (6,-8), (-1,-8)

$W = \sqrt{(6 - (-1))^{2} + (1 - 1)^{2}} = \sqrt{49} = 7$

The width is 7.

6 0

4 years ago

Read 2 more answers

Bob and Mark talk about their families. Bob says he has 3 kids, the product of their ages is 72. He gives another clue: the sum

Alenkasestr [34]

What is 72/3=24 24/3=8 8/3=3

6 0

4 years ago