Question

Find the necessary confidence interval for the binomial proportion p. (Round your answers to three decimal places.) A 90% confidence interval for p, based on a random sample of n = 500 observations from a binomial population with x = 337 successes. to Interpret the interval that you have constructed. A - In repeated sampling, 90% of all intervals constructed in this manner will enclose the population proportion. B - There is a 10% chance that an individual sample proportion will fall within the interval. C - There is a 90% chance that an individual sample proportion will fall within the interval. D - 90% of all sample proportions will fall within the interval. E - In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.

          Find the necessary confidence interval for the binomial
proportion p. (Round your answers to three decimal
places.)
A 90% confidence interval for p, based on a random
sample of n = 500 observations from a binomial population
with
x = 337
successes.
______ to ______
Interpret the interval that you have constructed.
A - In repeated sampling, 90% of all intervals constructed in
this manner will enclose the population proportion.
B - There is a 10% chance that an individual sample proportion
will fall within the interval.    
C - There is a 90% chance that an individual sample proportion
will fall within the interval.
D - 90% of all sample proportions will fall within the
interval.
E - In repeated sampling, 10% of all intervals constructed in
this manner will enclose the population proportion.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ajiboye Tunde

03/02/2022

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Find the necessary confidence interval for the binomial proportion p. (Round your answers to three decimal places.) A 90% confidence interval for p, based on a random sample of n = 500 observations from a binomial population with x = 337 successes. ______ to ______ Interpret the interval that you have constructed. A - In repeated sampling, 90% of all intervals constructed in this manner will enclose the population proportion. B - There is a 10% chance that an individual sample proportion will fall within the interval. C - There is a 90% chance that an individual sample proportion will fall within the interval. D - 90% of all sample proportions will fall within the interval. E - In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.

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00:01 So our question says that i find the necessary confidence interval for the binomial proportion p.

00:05 Round your answers to three decimal place.

00:07 A 90 % confidence interval of p based on the random sample of n is equals to 500 observations from a binomial population with x is equals to 337 successes is worth.

00:18 Then we are also supposed to interpret our confidence interval.

00:22 So from this question we have our sample size n to be crossed to 500 and we have this x to be cost to 337.

00:30 So that means our sample proportion p -cap is actually going to be cost to 337 divided by 500.

00:37 When we do the match, we have that to be cost to 0 .74.

00:41 So to construct our confidence interval for a single value of population proportion, we have the formula that says p is equal to p -cap plus or minus the critical value times the square root of p -cap, q -cap divided by n.

00:55 Alright, so we need our critical value and we should also know that our q -cap is going to be caused to be caused to the square root of p -cup, we need our q -cap is going to be caused to be cost to the square root of the cost.

01:01 To 1 minus 0 .674 and that gives us 0 .3 to 6.

01:06 So for our critical value we need to know the type of distribution that defines our data sets.

01:12 Take a look at our sample size.

01:14 We have a very large sample size and also a very large number of success.

01:17 So definitely our critical value cv is going to be a z score...

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