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2 years ago

You collect a random sample of size n from a population and calculate a 95% confidence

1 answer:

4 0

A strategy which would produce a new confidence interval with an <u>increased</u> margin of error is to: A. use a 98% confidence level.

<h3>What is a confidence interval?</h3>

A confidence interval simply refers to a range of estimated values which defines the probability that a population parameter will lie within it.

<h3>How to calculate the margin of error?</h3>

Mathematically, a margin of error is calculated by using this formula:

$MOE_{\gamma}=Z_{\gamma} \times \sqrt{\frac{\sigma^2}{n} }$

From the above formula, we can deduce that the margin of error is directly proportional to the critical value and inversely proportional to the square root of sample size.

This ultimately implies that, increasing the confidence level from 95% to 98% would <u>increase</u> the critical value and by extension the margin of error and vice-versa.

Read more on confidence interval here: brainly.com/question/25779324

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The data given to the right includes data from candies, and of them are red. The company that makes the candy claims that % of

Dafna1 [17]

Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:

$n = 39, \pi = \frac{8}{39} = 0.2051$

Hence the bounds of the interval are:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.3318$

As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

More can be learned about the z-distribution at brainly.com/question/25890103

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7 0

2 years ago

ANYONE GOOD AT MATH CAN PLEASE HELP ME???

dmitriy555 [2]

Answer:

i can help you

any time u want

6 0

2 years ago

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Two different floor plans are being offered in a new housing development. Several prospective

cricket20 [7]

Answer:

0.912

Step-by-step explanation:

<em>The complete question is attached.</em>

<em />

"OR" in probability means "ADDITION". So we find the individual probabilities and "ADD" them.

P(Plan A) would be the total people for plan A (add up column of Plan A) divided by total number of people [add up all the numbers].

Looking at the table, we have:

P (Plan A) = 38/68

Now,

P(40-49 Group) can be found by adding up the row of 40-49 age group and dividing by the total. So, we have:

P(40 - 49 Group) = 24/68

Now, adding up both:

38/68 + 24/68 = 62/68 = 0.912

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2 years ago

Select the statement that describes this expression: 13 + fraction 1 over 2 x (6 ÷ 2 + 6)

amid [387]

I think the answer is B

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3 years ago

Read 2 more answers

Solve the problem below

wlad13 [49]

Answer:

(5,0)

Step-by-step explanation:

an x-intercept is where the line crosses the x-axis. in this case it crosses it multiple time so other possible answers could be (1,0) or (-1,0)

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3 years ago