Graduate Programs in Statistics! 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 8282 US statistics or biostatistics doctoral programs for which enrollment data were available.¹ The dataset Statistics Grad Schools lists all these schools together with the total enrollment of full-time graduate students in each program in 2009. Click here for the dataset StatisticsPhD associated with this question. If using StatKey, the data needed is preloaded as Statistics Grad Schools in the drop-down menu in the upper left corner. Click here to access StatKey. ¹Full list of the 82 Group IV departments was obtained at http://www.ams.org/profession/data/annual-survey/group_iv. Data on enrollment obtained primarily from Assistantships and Graduate Fellowships in the Mathematical Sciences, 2009, American Mathematical Society. The list does not include combined departments of mathematics and statistics and does not include departments that did not reply to the AMS survey.

(a) A random sample of 1010 of the 8282 enrollment values is given in the table below. Give the notation for the sample mean.

University	Department	Enrollment
Case Western Reserve University	Statistics	1111
University of South Carolina	Biostatistics	4545
Harvard University	Statistics	6767
University of California - Riverside	Statistics	5454
Medical University of South Carolina	Biostatistics	4646
University of Nebraska	Statistics	4444
New York University	Statistics	66
Columbia University	Statistics	196196
University of Iowa	Biostatistics	3535
Baylor University	Statistics	2626

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(b) Compute the sample mean. Enter the exact answer. Sample mean==

(c) Another random sample of 1010 of the 8282 enrollment values is given in the table below. Give the notation for this sample mean.

University	Department	Enrollment
University of Wisconsin	Statistics	116116
Cornell University	Statistics	7878
Yale University	Statistics	3636
Iowa State University	Statistics	145145
Boston University	Biostatistics	3939
University of Nebraska	Statistics	4444
University of Minnesota	Biostatistics	4848
University of California - Los Angeles	Biostatistics	6060
University of California - Davis	Statistics	3434
Virginia Commonwealth University	Statistics	1515

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(d) Compute the sample mean. Enter the exact answer. Sample mean ==

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(e) Give the notation for the mean enrollment value for the entire population of these 8282 graduate programs.

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(f) Find the mean enrollment value for the entire population of these 8282 graduate programs. Round your answer to two decimal places. Mean==

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(g) Consider the sampling distribution if we calculate many sample means taking samples of size n=10n=10 from this population of enrollment values. What shape will it have?

Skewed to the left

Skewed to the right

Symmetric and bell-shaped

Symmetric but not bell-shaped

None of these

(h) Where will the sampling distribution be centered? Round your answer to two decimal places. Center==

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