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The figure illustrates two sampling distributions for sample proportions when

The figure illustrates two sampling distributions for sample proportions when the population proportion p = 0.50.

a. Find the standard deviation for the sampling distribution of the sample proportion with (i) n = 100 and (ii) n = 1000.

b. Explain why the sample proportion would be very likely (as the figure suggests) to fall (i) between 0.35 and 0.65 when n = 100, and (ii) between 0.45 and 0.55 when n = 1000. (Recall that for an approximately normal distribution, nearly the entire distribution is within 3 standard deviations of the mean.)

c. Explain how the results in part b indicate that the sample proportion tends to more precisely estimate the population proportion when the sample size is larger.

a. Find the standard deviation for the sampling distribution of the sample proportion with (i) n = 100 and (ii) n = 1000.

b. Explain why the sample proportion would be very likely (as the figure suggests) to fall (i) between 0.35 and 0.65 when n = 100, and (ii) between 0.45 and 0.55 when n = 1000. (Recall that for an approximately normal distribution, nearly the entire distribution is within 3 standard deviations of the mean.)

c. Explain how the results in part b indicate that the sample proportion tends to more precisely estimate the population proportion when the sample size is larger.

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