in one community 78% of the over 400000 people who speak spanish - In one community, 56% of the over 300,000 people who speak Spanish are native speakers. Suppose a politician took monthly random samples of 60 people in the community who speak Spanish and calculated the proportion \widehat{p} of people from each sample who were native Spanish speakers. What will be the shape of the sampling distribution of \widehat{p}?

Sangeetha Pulapaka (last edited 8 months ago) (Expert, Educator @Qalaxia)

We are looking at which conditions does the sampling distributions of the sample proportions, looks, skewed to the left, skewed to the right, approximately normal, or uniform.

We know that when we have, np≥10, and n(1−p)≥10, and both of these are true, where n is the sample size, and p is the sample of proportions, the sampling proportions of sample distributions, will be normal in shape.

Our sample size n = 60, and p = 0.56

Expected successes = np = 33.6 > 10

Expected failures = n(1-p) = 60 ( 1- 0.56) = 33.6 > 10

Since we expect at least 10 successes and 10 failures per sample, we have a normal sampling distribution.

The shape of the sampling distribution of \widehat{p} is approximately normal.

Please note: This question has been changed!

HERE IS THE EXACT SAME QUESTION AS IN KHAN'S ACADEMY

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