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 were82

US statistics or biostatistics doctoral programs for which enrollment data were available.¹The datasetStatisticsPhDlists all these schools together with the total enrollment of full-time graduate students in each program in 2009.

Clickherefor the dataset associated with this question.

Clickhereto accessStatKey.

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 fromAssistantships 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 of10

of the82

enrollment values is given in the table below. Give the notation for the sample mean.

UniversityDepartmentEnrollmentYale UniversityStatistics

36

Iowa State UniversityStatistics145

Harvard UniversityStatistics

67

University of California - RiversideStatistics

54

University of California - Los AngelesBiostatistics

60

University of Nebraska

Statistics

44

Cornell UniversityStatistics78

Columbia UniversityStatistics196

University of California - DavisStatistics34

Virginia Commonwealth UniversityStatistics

15

SHOW HINT

LINK TO TEXT

(b) Compute the sample mean.

Enter the exact answer.

Sample mean=

exact number, no tolerance

SHOW HINT

LINK TO TEXT

(c) Another random sample of10

of the82

enrollment values is given in the table below. Give the notation for this sample mean.

UniversityDepartmentEnrollmentUniversity of WisconsinStatistics

116

New York UniversityStatistics

6

Case Western Reserve UniversityStatistics

11

University of South CarolinaBiostatistics45

Boston UniversityBiostatistics39

University of Nebraska

Statistics

44

University of MinnesotaBiostatistics48

Medical University of South CarolinaBiostatistics

46

University of IowaBiostatistics35

Baylor UniversityStatistics

26

SHOW HINT

LINK TO TEXT

(d) Compute the sample mean.

Enter the exact answer.

Sample mean=

exact number, no tolerance

SHOW HINT

LINK TO TEXT

(e) Give the notation for the mean enrollment value for the entire population of these82

graduate programs.

SHOW HINT

LINK TO TEXT

(f) Find the mean enrollment value for the entire population of these82

graduate programs.

Round your answer to two decimal places.

Mean=

the absolute tolerance is +/-0.1

SHOW HINT

LINK TO TEXT

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

=

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

SHOW HINT

LINK TO TEXT

(h) Where will the sampling distribution be centered?

Round your answer to two decimal places.

Center=

the absolute tolerance is +/-0.5

Click if you would like to Show Work for this question:Open Show Work