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Anautomotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic In an earlier study the population proportion was est...

Question

Anautomotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic In an earlier study the population proportion was estimated to be 0.31. How large a sample would be required in order to estimate the fraction of new car buyers who prefer foreign cars at the 95% confidence level with an error of at most 0.03?

Anautomotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic In an earlier study the population proportion was estimated to be 0.31. How large a sample would be required in order to estimate the fraction of new car buyers who prefer foreign cars at the 95% confidence level with an error of at most 0.03?



Answers

A government agency wishes to estimate the proportion of drivers aged $16-24$ who have been involved in a traffic accident in the last year. It wishes to make the estimate to within one percentage point and at $90 \%$ confidence. Find the minimum sample size required, using the information that several years ago the proportion was 0.12 .

Welcome to this list In this lesson. We're given the margin of error as 0.05. Then the disease called for they need to go less than 90 5% interval would be 1.96. And we have ah population proportions been nice. Zero 35. So what we are looking for is the sample size. Yeah, we can square both sides. Oh yeah. The square. What is equal these four square 10 times proportion by the one minus portion all of than the end. Yeah. Cool. And the proportion I am one my all over Michael Barrows. I mean thing or those values. Some point Yeah. Their point right. One minute all. So five square we have value that is giving us for nine. Very under them. Really very under that. So that should be also all right. Time for a time. This is the end of the lesson.

We want to calculate at 95% confidence the population proportion P with an accuracy within 5%. We want to find the minimum sample size and needed to accomplish this for a no estimate of the proportion P hat be a test statistic of P hat from a survey results or other data of 50.28 And see we want to compare the answers from A and B. So to get started we need to be able to solve A and B. Using the formula if I hear and equals P. Hat you hat times over E squared E. Is the marginal 0.5 M. Z is the critical value related to our confidence level which we can find from a Z. Table or a standard normal distribution. So Z of 95% is 1.96 So now we plug in to a. Where he had equals equals 0.5. Because we have no estimate we obtained and equals 385. For B. We plug in P had equals 3850.28 Q is equal 2.72 and we get and is 303 comparing answers. We see that ended slightly larger for NOPD.


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