sampling distribution of sample proportions - According to a newspaper survey, about 9 % 9%9, percent of the local residents order groceries online at least once a month. Suppose we took random samples of n = 80 n=80n, equals, 80 residents from this population and computed the proportion p ^ p ^ p, with, hat, on top of residents in each sample who order groceries online at least once a month. We can assume the newspaper's claim is true. Which of the following distributions is the best approximation of the sampling distribution of p ^

According to a newspaper survey, about 9 % 9%9, percent of the local residents order groceries online at least once a month. Suppose we took random samples of n = 80 n=80n, equals, 80 residents from this population and computed the proportion p ^ p ^ p, with, hat, on top of residents in each sample who order groceries online at least once a month. We can assume the newspaper's claim is true. Which of the following distributions is the best approximation of the sampling distribution of p ^

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Sangeetha Pulapaka (last edited 1 year 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.

Our sample size n = 0,09 and p = 80.

Expected successes np = 0.09(80) = 7.2

Expected failures n(1-p) = 80( 1- 0.09) = 80(0.91) = 72.8

Since np\lt 10, and n(1-p) \geq 10, the shape of the sampling proportion is not normal.

Now to find in which direction the shape of the sampling distribution is skewed.

We would expect only a right-skewed sampling distribution when the population proportion is so extreme relative to the sample size that there are fewer than 10 expected successes per sample. So, since our expected successes is less than 10, we have a right-skewed sampling distribution.

Do have a look at the below discussion to understand the shape of a right-skewed sampling distribution.

https://www.qalaxia.com/viewDiscussion?messageId=606489b2f4d26b0f37dbd958

Qalaxia Master Bot (last edited 1 year ago)

I found an answer from www.khanacademy.org

Normal conditions for sampling distributions of sample proportions ...

AP.STATS: UNC‑3 (EU). ,. UNC‑3.L (LO). ,. UNC‑3.L.1 (EK). About Transcript. Conditions for roughly normal sampling distribution of sample proportions.

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