The area of Norway is 24% more than the area of Colorado so Norway's area is-------% of Colorado's area

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Part 1

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

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 on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

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 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 on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22$

And rounded up we have that n=426

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2 years ago

Jane wants to add chocolate chips to her trail mix. A 3-pound bag of chocolate chips costs $3.22. What is the unit price?

IrinaVladis [17]

Answer:

$1.07 per bag

Step-by-step explanation:

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2 years ago

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You’re assembling desserts with a friend. Together you can make 12 desserts in five minutes. Two more friends arrive and you are

Dafna1 [17]

Well there's 10 minutes in the second part so first 48/2 is 24. Now 24/4 (since there's 4 people so far) is 6, now 6*6 because there's now 6 people in total so the final answer is 36 in 5 minutes

8 0

2 years ago

The expression 11(1.022)^t11(1.022)

Lena [83]

Answer: growth factor = 1.022

Step-by-step explanation:

The expression 11(1.022)^t is an exponential expression where the rate of increase is 2.2%

What 1.022 represent in this equation is the growth factor of per capita gross domestic product (GDP) of the US

6 0

2 years ago

A train traveled 260 miles in 4 hours. If the train’s average rate of travel increases by 12 mph, what is its new average rate o

jasenka [17]

Answer:

Correct option A

Step-by-step explanation:

Average rate = 260/4 = 65 mph

It increases by 12mph

So 65+12 = 77 mph

Correct option A

8 0

2 years ago

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