Suppose a simple random sample of size n = 75 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.6. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Determine the mean of the sampling distribution of $\hat{p}$. $\mu_{\hat{p}} = $ (Round to one decimal place as needed.)
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Step 1: The mean of the sampling distribution of p is equal to the population proportion p. Show more…
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Suppose a simple random sample of size n = 150 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic is p = 0.4. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). B. Not normal because n ≤ 0.05N and np(1 - p) ≥ 10. C. Approximately normal because n ≤ 0.05N and np(1 - p) ≥ 10. D. Not normal because n ≤ 0.05N and np(1 - p) < 10. Determine the mean of the sampling distribution of p̂. μp̂ = 0.4 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p̂. σp̂ = 0.04 (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 66 or more individuals with the characteristic? That is, what is P(p̂ ≥ 0.44)? P(p̂ ≥ 0.44) = 0.1587 (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 51 or fewer individuals with the characteristic? That is, what is P(p̂ ≤ 0.34)? P(p̂ ≤ 0.34) = (Round to four decimal places as needed.)
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Population whose size is N = 20,000 and whose population proportion with specified characteristic is p = 0.4. Suppose a simple random sample of size n = 200 is obtained. (a) Describe the sampling distribution of P. Choose the phrase that best describes the shape of the sampling distribution below: 0A: Approximately normal because n = 0.5N and np(1 - p) < 10. Approximately normal because n > 0.05N and np(1 - p) < 10. Not normal because n < 0.05N and np(1 - p) > 10. Not normal because n < 0.05N and np(1 - p) < 10. Determine the mean of the sampling distribution of p (Round to one decimal place as needed). Determine the standard deviation of the sampling distribution of p (Round to six decimal places as needed).
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