Question

490/654 Venezuelan women from the armed forces said they were not interested in American Football. A...

490/654 Venezuelan women from the armed forces said they were not interested in American Football. A 95% confidence interval for the proportion with no interest in American Football is 0.70 to 0.80.

A) What would margin of error be for the CI of this proportion?
Wouldn't this just be 10%?

B) We then sampled 1568 more Venezuelan woman. They were also asked if they had interest in American Football. If we constructed another CI based on this sample, how would its width compare to the width of the confidence interval based on the 654 originally sampled women?
Wouldn’t the confidence interval width become smaller due to a more accurate estimate from the greater sample size of the same population of women?

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