How many gallons of water are in the Pacific Ocean?

3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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

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

Solution to the problem

We assume for this case a confidence level of 95%. 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:

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

The margin of error for the proportion interval is given by this formula:

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

And if we replace the values obtained we got this:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

6 0

3 years ago

Is is the square root of 47 irrational or rational

scoray [572]

<span>the square root of is 47 irrational</span>

5 0

3 years ago

Read 2 more answers

Factorise x²+8x+12plz give answer

larisa86 [58]

Answer:

(x+6)(x+2)

Step-by-step explanation:

we have

ax²+bx+c

To factor parabolas we need to find a number that adds to b (or 8) and mulitplies to a*c (or 12)

The numbers 6 and 2 fit this criteria which means we have

(x+6)(x+2)

7 0

3 years ago

Read 2 more answers

Kayleigh has $4500 in a savings account at the bank that earns 0.8% interest per year. How much

Sloan [31]

Answer:

Kayleigh will have a total of $4608.

Step-by-step explanation:

First, you use the formula, I=PRT (Interest=Principal, Rate, Time), then you distribute the numbers: (I=4500x0.8%x3) when you multiply them all, you get $108, then you lastly add 108 to 4500, and you get your final answer of $4608.

7 0

3 years ago

Read 2 more answers

The population of a town is 15,000. It decreases at a rate of 8% per year. In about how many years

Paha777 [63]

Answer:

5

Step-by-step explanation:

If a population is decreasing by 8% we can multiply the population by 92% (1-.08)

which means we have the following equation

population=15000(.92)ⁿ

where n is the number of years

we want to know when the population will be 10,000 so we write

10,000=15,000(.92)ⁿ

.66667=.92ⁿ

a rule we have is

$n=y^x\\log_yn=x$

which means that

$.66667=.92^n\\=log_{.92}.66667$

compute this and get

4.867

round this up to 5

4 0

3 years ago