Make a confidence interval for ppp given the following values.x=314,n=500,C=99%x=314,n=500,C=99\%x=314,n=500,C=99%

( 0.572 , 0.684 ) \left(0.572,0.684\right) ( 0.572 , 0.684 )

Make a confidence interval for p p p given the following values. x = 314 , n = 500 , C = 99 % x=314,n=500,C=99\% x = 314 , n = 500 , C = 99%

Welcome to the practice. For this problem, we'd like to find the confidence interval for p, our population proportion, given the following information. We know that x is 314, n is 500, and c, our confidence level, is 99%. Let's use the same steps we had from the concept video to find it on our t I 80 fours. I'm gonna pull out my calculator and click on the stat button, then scroll two to the right to get to the test menu. That's step one. All set. I want option a, the one dash prophecy interval function. So I'm just gonna scroll down to it. And once I get there, I will click enter. That's step two. All set. Now I just need to enter in some information about the problem. X is 314, n is 500, and our confidence level is 0.99. Once that's accurate, I'm just gonna scroll down to calculate and click enter. That's step three all set, and I'll see my confidence interval appear in my viewing window. I can see that it is approximately between zero point five seven two and zero point six eight four. Awesome work.

Make a confidence interval for p p p given the following values. x = 314 , n = 500 , C = 99 % x=314,n=500,C=99\% x = 314 , n = 500 , C = 99%

( 0.572 , 0.684 ) \left(0.572,0.684\right) ( 0.572 , 0.684 )

( 0.560 , 0.696 ) \left(0.560,0.696\right) ( 0.560 , 0.696 )

( 0.572 , 0.696 ) \left(0.572,0.696\right) ( 0.572 , 0.696 )

( 0.560 , 0.684 ) \left(0.560,0.684\right) ( 0.560 , 0.684 )

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion

Statistics for Business

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion

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Multiple Choice

Make a confidence interval for $p$ given the following values.
$x=314,n=500,C=99\%$

$\left(0.560,0.696\right)$

$\left(0.572,0.684\right)$

$\left(0.572,0.696\right)$

$\left(0.560,0.684\right)$

Verified step by step guidance

Step 1: Identify the given values in the problem. Here, the sample proportion (p̂) is calculated as p̂ = x/n, where x = 314 and n = 500. The confidence level (C) is 99%.

Step 2: Determine the critical value (z*) for a 99% confidence level. This can be found using a z-table or statistical software. For a 99% confidence level, z* is approximately 2.576.

Step 3: Calculate the standard error (SE) of the sample proportion using the formula SE = sqrt((p̂ * (1 - p̂)) / n). Substitute the values of p̂ and n into the formula.

Step 4: Compute the margin of error (ME) using the formula ME = z* * SE. Multiply the critical value (z*) by the standard error (SE) to find the margin of error.

Step 5: Construct the confidence interval (CI) using the formula CI = (p̂ - ME, p̂ + ME). Subtract and add the margin of error (ME) to the sample proportion (p̂) to find the lower and upper bounds of the confidence interval.

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