One of the many wonderful things about studying statistics is that graduate programs in statistics often pay their graduate students, which means that many graduate students in statistics are able to attend graduate school tuition free with an assistantship or fellowship. In 2009, there were 82 US statistics or biostatistics doctoral programs for which enrollment data were available. The dataset StatisticsPhD lists all these schools together with the total enrollment of full-time graduate students in each program in 2009 (a) Use StatKey or other technology to select a random sample of 10 of the 82 enrollment values. Indicate which values you've selected and compute the sample mean.
(b) Repeat part (a) by taking a second sample and calculating the mean
(c) Find the mean enrollment for the entire population of these 82 graduate programs. Use correct notation for your answer. Comment on the accuracy of using the sample means found in parts (a) and (b) to estimate the population mean.
(d) Use Statkey or other technology to generate a sampling distribution. Generate 5000 sample proportions. Give the shape and center of the sampling distribution and give the standard error
(e) What does each dot on the sampling distribution generated in part (d) represent?
(f) Findthe interval that contains approximately 95% of all sample means using the standard error and the center from part d.
(g) In each case, indicate whether each value is (i) reasonably likely to occur from this size, (ii) unusual but might occur occasionally, or (ii) extremely unlikely to ever occur 55, 45, 80, 100,3 25,and 150