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Chapter 3, Section 1, Exercise 031

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 82 US statistics or biostatistics doctoral programs for which enrollment data were available.1 The dataset StatisticsPhD lists all these schools together with the total enrollment of full-time graduate students in each program in 2009. Click here for the dataset associated with this question. 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 10 of the 82 enrollment values is given in the table below. Give the notation for the sample mean.

University	Department	Enrollment
Case Western Reserve University	Statistics	11
University of South Carolina	Biostatistics	45
Harvard University	Statistics	67
University of California - Riverside	Statistics	54
Medical University of South Carolina	Biostatistics	46
University of Nebraska	Statistics	44
New York University	Statistics	6
University of Minnesota	Biostatistics	48
University of Iowa	Biostatistics	35
Cornell University	Statistics	78

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

exact number, no tolerance

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(c) Another random sample of 10 of the 82 enrollment values is given in the table below. Give the notation for this sample mean.

University	Department	Enrollment
University of Wisconsin	Statistics	116
Baylor University	Statistics	26
Yale University	Statistics	36
Iowa State University	Statistics	145
Boston University	Biostatistics	39
University of Nebraska	Statistics	44
Columbia University	Statistics	196
University of California - Los Angeles	Biostatistics	60
University of California - Davis	Statistics	34
Virginia Commonwealth University	Statistics	15

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

exact number, no tolerance

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(e) Give the notation for the mean enrollment value for the entire population of these 82 graduate programs.

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(f) Find the mean enrollment value for the entire population of these 82 graduate programs. Round your answer to two decimal places. Mean=

the absolute tolerance is +/-0.1

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(g) Consider the sampling distribution if we calculate many sample means taking samples of size n=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

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

the absolute tolerance is +/-0.5

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