The temperature went from -16°F to 7°F. What was the change in temperature?

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

X2+Y2=25

Fofino [41]

$x^{2} + y^{2} =25$ is equation of circle which have radius equal 5 and center in (0,0) point

8 0

3 years ago

A 40-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain

daser333 [38]

Answer:

a) W₁ = 78400 [J]

b)Wt = 82320 [J]

Step-by-step explanation:

a) W = ∫ f*dl general expression for work

If we have a chain with density of 10 Kg/m, distributed weight would be

9.8 m/s² * 10 kg = mg

Total length of th chain is 40 m, and the function of y at any time is

f(y) = (40 - y ) mg where ( 40 - y ) is te length of chain to be winded

At the beggining we have to wind 40 meters y = 0 at the end of the proccess y = 40 and there is nothing to wind then:

f(y) = mg* (40 - y )

W₁ = ∫f(y) * dy ⇒ W₁ = ∫₀⁴⁰ mg* (40 - y ) dy ⇒ W₁ = mg [ ∫₀⁴⁰ 40dy - ∫₀⁴⁰ ydy

W₁ = mg [ 40*y |₀⁴⁰ - 1/2 * y² |₀⁴⁰ ⇒ W₁ = mg* [ 40*40 - 1/2 (40)² ]

W₁ = mg * [1/2] W₁ = 10*9,8* ( 800 )

W₁ = 78400 [J]

b) Now we can calculate work to do if we have a 25 block and the chain is weightless

W₂ = ∫ mg* dy ⇒ W₂ = ∫₀⁴⁰ mg*dy ⇒ W₂ = mg y |₀⁴⁰

W₂ = mg* 40 = 10*9.8* 40

W₂ = 3920 [J]

Total work

Wt = W₁ + W₂ ⇒ Wt = 78400 + 3920

Wt = 82320 [J]

6 0

3 years ago

Old Navy is having a sale for the summer they are selling for shirts for $23 what is the price per share at the store

kirill115 [55]

Answer:

5 dollars and 75 cents.

Step-by-step explanation:

I think you mean 4 shirts are 23$? If so ,you would divide 23 by 4 to get how many dollars is 1 shirt. 23/4 = 5.75

8 0

3 years ago

What is the value of the expression 10-(1/2)^4•48

diamong [38]

Do I look like a math teacher, I hate math do you hate math?

4 0

3 years ago

Read 2 more answers