7.10 Effect of n on sample proportion 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. (Hint: 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 estimate the population proportion more precisely when the sample size is larger.

Transcribed Image Text:

n = 1000, showing sample proportion very likely to fall between 0.45 and 0.55 n = 100 T -Sample proportion 0.35 0.40 0.45 0.50 0.55 0.60 0.65 Population proportion