Question

In: Statistics and Probability

USA Today reported that about 47% of the general consumer population in the United States is...

  1. USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose that Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 503 said that they would buy another Chevrolet.

  1. Check the assumptions for constructing a confidence interval
  1. Construct a 90% confidence interval
  1. Construct a 95% confidence interval

  1. Construct a 99% confidence interval

  1. What happened to the margin of error as the confidence increased?

  1. How else can we change the margin of error without changing or the confidence?

  1. Which confidence intervals above agree with the claim that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice? Explain why?

Solutions

Expert Solution

a. Since the number of sample is 1006 we have enough sample thus we can use large sample approximations for calculating confidence interval

Construct a 90% confidence interval

Construct a 95% confidence interval

Construct a 99% confidence interval

Construct a 99% confidence interval

Thus it can be observed that the margin of error is increasing with increase in the level of confidence.

Margin of error can be changed with change in sample size as well

It can be observed that at a 95% level of significance 47% proportion falls within the confidence interval.

orchestra answered 1 year ago
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