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An automobile manufacturer wants to determine what proportion ofits customers are dissatisfied with the service received from theirlocal dealer. The manufacturerâ...

Question

An automobile manufacturer wants to determine what proportion ofits customers are dissatisfied with the service received from theirlocal dealer. The manufacturer’s manager doesn’t have anyestimate for the proportion of dissatisfied customers. Howmany customers should they sample if they want to be correct towithin 4% of the actual proportion with a 98% level ofconfidence?67984666845

An automobile manufacturer wants to determine what proportion of its customers are dissatisfied with the service received from their local dealer. The manufacturer’s manager doesn’t have any estimate for the proportion of dissatisfied customers. How many customers should they sample if they want to be correct to within 4% of the actual proportion with a 98% level of confidence? 67 9 846 66 845



Answers

Overseas Travel A researcher wishes to be 95\% confident that her estimate of the true proportion of individuals who travel overseas is within $4 \%$ of the true proportion. Find the sample necessary if, in a prior study, a sample of 200 people showed that 40 traveled overseas last year. If no estimate of the sample proportion is available, how large should the sample be?

In this question, we have to determine the sample sizes. The first one is at 95% confidence level at in part A. It's 95% confidence level. Which means my Alfa is zero point my Alfa 0.0 fight. This means that my Alfa by two is 0.2 fight. Okay, what is the margin of error? The margin of error e is given us. This is given other formulas e alfa by two Sigma by route and Z Alfa by two into sigma by route. And now N is what we want to find out. We know the value off the alphabet. How do we find that we use a critical value calculator and we put our value as 0.25 and the critical value for this turns out to be 1.96 This is 1.9 1.96 Now what is Sigma Sigma? Standard deviation And we are being told that we have to use a planning value for the population standard deviation off eight minutes. So I signifies it. So our margin of error has to be within two minutes, right? Yeah, this has to be within two minutes. And l z l four by two is 1.96 multiplied by sigma, which happens to be eight upon route. And now this is the value that I want to find out off route and And when I use the calculator, the value that I get is any is equal to 60 do and is equal to 62. This is the sample size that is required now when I want 99% confidence level. What is going to be my Alfa? By to my first of all, my Alfa 0.10 point 01 which means that my Alfa by two is 0.5 So what is going to be the critical value for this? Given Alfa by two it is 2.5 two points. Fight if I take it again, it is 2.575 2.575 Eat. All right, We just put in the values this is imagine, Offender, This is critical value multiplied by Sigma's eight upon Route 10. This is what we're gonna find out. What is the logic? Tell us what should happen Okay. Our sample size should increase right because we want to be more confident. So which means that our sample size should increase. So if I use a calculator for this, I'm getting my end as 107 My end is turning out to be close to 107 So this is a sample size that I required if I want to be 99% conflict.

Hi. The claim is best 90% off customer were served by the department Are please on were given that the from the survey 14 We're dissatisfied from from the service eso we want toe find the confidence and terrible office or eso. Here's the formula and as because he hates it ALF over two. So our over is bored over five and from the table this is 1.96 eso their confidence and terrible is for the dissatisfied is from 0.1 to sex toe 134 or three on for part B. We can say that the service little bit overestimated older Mr Mid Obsessed five customer


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