Question

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.02 margin of error at a 80% level of confidence. a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number. n = households b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of $\hat{p} = 0.2$. Using this new information. what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number. n = households

          You work for a marketing firm that has a large client in the automobile industry. You have been asked to
estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned
to gather a random sample that could be used to estimate this proportion to within a 0.02 margin of error
at a 80% level of confidence.
a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error?
Round your answer up to the nearest whole number.
n = 
households
b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required.
You conduct a small preliminary sample, and you obtain a sample proportion of $\hat{p} = 0.2$. Using this new
information. what sample size should you gather in order to obtain a 0.02 margin of error? Round your
answer up to the nearest whole number.
n = 
households

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You work for a marketing firm that has a large client in the automobile industry. You have been asked to
estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned
to gather a random sample that could be used to estimate this proportion to within a 0.02 margin of error
at a 80% level of confidence.
a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error?
Round your answer up to the nearest whole number.
n =
households
b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required.
You conduct a small preliminary sample, and you obtain a sample proportion of p̂ = 0.2. Using this new
information. what sample size should you gather in order to obtain a 0.02 margin of error? Round your
answer up to the nearest whole number.
n =
households

Added by Esperanza F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ariana Nash

12/17/2022

Step 1

02 margin of error at an 80% level of confidence, we can use the formula: n = (Z^2 * p * (1-p)) / E^2 Where: n = sample size Z = z-score corresponding to the level of confidence (80% level of confidence corresponds to a z-score of 1.28) p = estimated proportion Show more…

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You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.02 margin of error at an 80% level of confidence. a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number. n = households b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of p = 0.2. Using this new information, what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number. n = households

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Transcript

00:01 Okay, so here we are told that we are going to make a confidence interval, and we need to get a random sample.

00:09 It's for a proportion, okay? and we're told that we want no bigger than a margin of error of 0 .02, and we want 98 % confidence.

00:21 And we have no prior research.

00:24 Okay? so in general, the confidence interval for a proportion is p -hat plus or minus the confidence.

00:30 Z star times the square root of p hat times one minus p hat over n.

00:38 Okay, this part here is the margin of error.

00:43 Okay, so we want that thing to be no more than 0 .02.

00:47 So i'm going to make an equation.

00:50 0 .02 equals z star times the square root of p times 1 minus p over n.

00:58 Remember, i don't know what p is, right? so i'm just going to like put that as a p star and give the most conservative estimate that i can for p, which is going to be 0 .5.

01:10 That's like, you know, just having 50 % of the sample be one way or the other.

01:15 So p star is going to be 0 .5.

01:18 Z star for 98 % confidence is always going to be the same thing.

01:23 And if i just look that up on my chart for critical values for z, that z star is 2 .326.

01:30 Okay.

01:30 So now i have pretty much everything i need to solve for n because i know that 0 .02, which is the margin of error, has to equal 2 .326 times the square root of 0 .5 times 1 minus 0 .5 divided by n.

01:48 Right? so i'm just going to do some algebra now to solve for n.

01:53 So if i divide both sides by 2 .326, i get 0 .02 over 2 .326.

02:01 Equals the square root of 0 .5 times 1 minus 0 .5, which that's actually 0 .25 if i multiply that out, right? so 0 .25 over n.

02:14 Now i'm going to square both sides...

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