2 (5) The dotplot below is a sampling distribution of sample proportions from random samples of size n = 200 from a population. Sampling Dotplot of Proportion. (a) 80 70 60 50 40 30 20 10 0.100 P= Left Tail Two Tail Right Tail 0.125 0.150 0.175 0.200 0.225 0.250 samples-1000 mean-0.199 std. error-0.028 0.275 Use the dotplot to estimate the value of the population proportion. p = 0.213, 1 (b) Use the 95% rule and the standard error SE= 0.028 to give an interval which contains roughly 95% of the sample proportions in the sampling distribution. (c) If the samples instead had size n = 50, what effect would this have on the mean and standard error of the sampling distribution? (d) Are the following sample proportions reasonably likely to occur, fairly un- likely to occur, or extremely unlikely to occur? p = 0.005, p= 0.276

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