7.Suppose the population proportion is 0.200.20 . If the sample size is equal to 5050 , what is the approximate sampling distribution of the sample proportion, P̂ 𝑃^ ?Multiple choice 5 Question 3 N(0.20,0.16)𝑁(0.20,0.16) N(0.20,0.0032)𝑁(0.20,0.0032) N(0.20,0.057)𝑁(0.20,0.057) N(0.80,0.16)𝑁(0.80,0.16)
Question
7.Suppose the population proportion is 0.200.20 . If the sample size is equal to 5050 , what is the approximate sampling distribution of the sample proportion, P̂ 𝑃^ ?Multiple choice 5 Question 3 N(0.20,0.16)𝑁(0.20,0.16) N(0.20,0.0032)𝑁(0.20,0.0032) N(0.20,0.057)𝑁(0.20,0.057) N(0.80,0.16)𝑁(0.80,0.16)
Solution
The sampling distribution of the sample proportion, P̂, is approximately normally distributed (N) with a mean equal to the population proportion (0.20) and a variance equal to the population proportion times (1 - the population proportion) divided by the sample size.
Step 1: Calculate the mean (μ) The mean of the sampling distribution (μ) is equal to the population proportion. So, μ = 0.20
Step 2: Calculate the variance (σ^2) The variance of the sampling distribution (σ^2) is calculated as: (population proportion * (1 - population proportion)) / sample size So, σ^2 = (0.20 * (1 - 0.20)) / 50 = 0.20 * 0.80 / 50 = 0.0032
Therefore, the approximate sampling distribution of the sample proportion, P̂, is N(0.20, 0.0032).
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