A random sample of n = 83 measurements is drawn from binomial population with probability of success 0.4. Complete parts a through d below: a. Give the mean and standard deviation of the sampling distribution of the sample proportion, p. The mean of the sampling distribution of p is. The standard deviation of the sampling distribution of p is (Round to four decimal places as needed.) b. Describe the shape of the sampling distribution of p. The shape of the sampling distribution of p is approximately normal because the sample size is small. The shape of the sampling distribution of p is approximately normal because the sample size is large. The shape of the sampling distribution of p is approximately uniform because the sample size is small. The shape of the sampling distribution of p is approximately uniform because the sample size is large. c. Calculate the standard normal z-score corresponding to a value of p=0.41. The standard normal z-score corresponding to a value of p=0.41 is (Round to two decimal places as needed.) d. Find P (p>0.41)
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A random sample of n = 71 measurements is drawn from a binomial population with probability of success 0.3. Complete parts a through d below. a. Give the mean and standard deviation of the sampling distribution of the sample proportion, p̂. The mean of the sampling distribution of p̂ is []. The standard deviation of the sampling distribution of p̂ is []. (Round to four decimal places as needed.) b. Describe the shape of the sampling distribution of p̂. A. The shape of the sampling distribution of p̂ is approximately uniform because the sample size is small. B. The shape of the sampling distribution of p̂ is approximately uniform because the sample size is large. C. The shape of the sampling distribution of p̂ is approximately normal because the sample size is large. D. The shape of the sampling distribution of p̂ is approximately normal because the sample size is small. c. Calculate the standard normal z-score corresponding to a value of p̂ = 0.35. The standard normal z-score corresponding to a value of p̂ = 0.35 is []. (Round to two decimal places as needed.) d. Find P (p̂ > 0.35). The probability that p̂ is greater than 0.35 is []. (Round to four decimal places as needed.)
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Use the same population of {4, 5, 9} that was used in Examples 1 and 5. As in Examples 1 and 5, assume that samples of size n = 2 are randomly selected with replacement. Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places. a. Find the value of the population standard deviation ? . b. Table 6Â3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s that are the same, as in Table 6Â4. (Hint: See Example 1 for Tables 6Â3 and 6Â4 that describe the sampling distribution of the sample mean.) c. Find the mean of the sampling distribution of the sample standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?
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