QUICK ITS TIMED WILL GIVE BRAINLYIST

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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

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

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 $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

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 $ME =\pm 0.06$ 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)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968$

And rounded up we have that n=170

6 0

4 years ago

This is Mathematics 800

Lena [83]

Answer:

It is possible to get all 8 in one go. However, it is very unlikely because...

Step-by-step explanation:

You have a 1/8 chance of getting the dinosaur you want from a box. That means obviously you are significantly more likely to get another less dinosaur. Which it likely won't have lasers and stuff. Which is always sad.

The theoretical probability is far less likely to actually happen than the experimental probability.

8 0

3 years ago

The diagram below represents changes that take place within the human body. The diagram

il63 [147K]

Answer:

Dynamic equilibrium

Step-by-step explanation:

Dynamic equilibrium in the human body is achieved when there is an internal control which tends to oppose certain outside forces which could affect the body. It's known to be the ability to detect and respond to stimuli by living organisms. When these stimuli occur, there are feedbacks or responses that are sent or received by the body to maintain stability. This dynamic equilibrium of the internal environment can also be seen as homeostasis.

3 0

3 years ago

40 points!!! please tell me how to do it not what the answer is :D

Julli [10]

Answer:

C

Step-by-step explanation:

You first distribute within the parentheses which is -(-z-2). This is going to make everything positive as everything in the parentheses is negative. You should get z+2. Next, you plug that back in. It should be-3z+z+2. You simplify to get -2z+2. Hope this helps!

5 0

3 years ago

Read 2 more answers

Hana buys a new dress for $40. how much does she pay if there is a 7% tax

Rzqust [24]

Answer:

$42.80

Step-by-step explanation:

We can set up an equation to solve this as such

$40*1.07=42.80$

6 0

3 years ago