In a recent poll, 390 people were asked if they liked dogs, and 71% said they did. Find the margin of error of this poll, at the 90% confidence level.

Question

what is the margin of error

Answer 1

critical z probability = midpoint between CL and 100% = 95%

critical z = 1.96

standard error = sqrt(phat * (1-phat)/n), where phat = 0.71 and n = 390

ME = critical z * standard error

Answer 2

Hey John!

This question is asking about the margin of error, which is equal to the sample statistic times the standard error. (Normally denoted as IMAGE: https://bit.ly/3aOHGsl)

In this specific problem, since we know that there are 390 people in the poll, we can use the central limit theorem to justify distribution of people in this survey is approximately normally distributed (n = 390 is greater than or equal to 30). This tells us that we need to use the z-statistic (denoted as z* or z star) as opposed to the t-statistic (denoted as t* or t star). Since we are given the confidence interval to be 90%, we can use a calculator or a z-statistics table to find that our z-statistic value is approximately 1.645 (z* = 1.645).

Now you may have noticed that the problem does not give us the standard deviation, but we are given the proportion of people that liked dogs. This shows that we need to use the one sample proportion statistics for the confidence interval. So in this case, (IMAGE: https://bit.ly/3ogbnW7) , where p-hat is the proportion of people that responded that they like dogs (p-hat = 0.71).

Plugging in all the numbers to the formula above should give you the answer.

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In short:

(IMAGE: https://bit.ly/3ogbnW7), where MOE is the margin of error, z* = 1.645, p-hat = 0.71, and n = 390.