Make a confidence interval for ppp given the following values.p^=0.15,n=60,C=90%p̂=0.15,n=60,C=90\%p^=0.15,n=60,C=90%

( 0.074 , 0.226 ) \left(0.074,0.226\right) ( 0.074 , 0.226 )

Make a confidence interval for p p p given the following values. p ^ = 0.15 , n = 60 , C = 90 % p̂=0.15,n=60,C=90\% p ^ = 0.15 , n = 60 , C = 90%

Welcome back. For this problem, we'll still be finding a confidence interval for p, our population proportion, but we've been given some different information. We have our sample proportion 0.15, our sample size at 60, and our confidence level at 90% or 0.9. We're going to use our t I 80 fours to find this confidence interval, but as a reminder, for step three, we'll have to enter in an x value, and we actually haven't been given that value. We'll have to use this formula here, which tells us that our sample proportion p hat is going to be equal to x divided by n, that sample size. So let's find our x value. We have that 0.15, that p hat value is going to be equal to x, which I don't know, divided by 60, our sample size. I'm going to multiply both sides by 60, and I'll end up getting nine is equal to x. Now I have my x value, my n value, and my c level, so I am all set to enter everything into my calculator. Let's pull those out and start by getting to the tests menu. I'm going to click on stat and scroll to the right, and that is step one, all set. For step two, I need to get to option a, which is my one dash prop c interval. So I'm just gonna scroll down to option a. And once I'm there, I'll click enter. That is step two. All set. You'll notice we still have the information from part a, so let's just switch it over to what we see in part b over here. We have our x value is nine, so I'm just gonna type nine right over that three fourteen. My new n value is 60, so let's put that in, and my new confidence level is 0.9. Once everything is accurate, I can scroll down to calculate and click enter, and I'll see my confidence interval appear in my viewing window. That's step three. All set. We can see that the interval is approximately 0.074 to 0.226. Awesome work.

Make a confidence interval for p p p given the following values. p ^ = 0.15 , n = 60 , C = 90 % p̂=0.15,n=60,C=90\% p ^ = 0.15 , n = 60 , C = 90%

( 0.074 , 0.226 ) \left(0.074,0.226\right) ( 0.074 , 0.226 )

( 0.055 , 0.245 ) \left(0.055,0.245\right) ( 0.055 , 0.245 )

( 0.074 , 0.245 ) \left(0.074,0.245\right) ( 0.074 , 0.245 )

( 0.055 , 0.226 ) \left(0.055,0.226\right) ( 0.055 , 0.226 )

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.
$p̂=0.15,n=60,C=90\%$

$\left(0.055,0.245\right)$

$\left(0.074,0.245\right)$

$\left(0.074,0.226\right)$

$\left(0.055,0.226\right)$

Verified step by step guidance

Step 1: Identify the given values in the problem. Here, the sample proportion is $ \hat{p} = 0.15 $, the sample size is $ n = 60 $, and the confidence level is $ C = 90\% $.

Step 2: Calculate the standard error (SE) of the sample proportion using the formula $ SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} $. Substitute $ \hat{p} = 0.15 $ and $ n = 60 $ into the formula.

Step 3: Determine the critical value (z*) for a 90% confidence level. For a 90% confidence interval, the critical value corresponds to the z-score that leaves 5% in each tail of the standard normal distribution. Use a z-table or statistical software to find $ z^* $.

Step 4: Compute the margin of error (ME) using the formula $ ME = z^* \cdot SE $. Multiply the critical value $ z^* $ by the standard error $ SE $ calculated in Step 2.

Step 5: Construct the confidence interval using the formula $ \text{Confidence Interval} = \hat{p} \pm ME $. Subtract the margin of error from $ \hat{p} $ to find the lower bound and add the margin of error to $ \hat{p} $ to find the upper bound.

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