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Lecture 3

# STA 205 Lecture Notes - Lecture 3: Binge Drinking, Sampling Distribution, National Safety CouncilExam

Department
Statistics
Course Code
STA 205
Professor
Brooke Buckley
Lecture
3

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Packet 3: Sampling Distribution of the Sample Proportion Textbook pages: 399 â€“ 406
After completing this material, you should be able to:
â€¢ explain what the symbols
p
Ë†
, p,
p
Ë†
Âµ
and
p
Ë†
Ïƒ
represent.
â€¢ describe the sampling distribution of the sample proportion by discussing its shape, mean, and standard deviation.
â€¢ find probabilities associated with various sample proportions based on the sampling distribution.
â€¢ make inferences from the probability and explain the reasoning.
A university is concerned with the percentage of its students who binge drink. Two different campus offices take samples
in order to investigate the severity of the problem. Students in each sample were asked whether or not they had engaged
in binge drinking (5 drinks at a sitting for men, 4 for women) in the past month. Results from the two surveys are
summarized in the relative frequency bar graphs below:
For each of the two samples, determine the sample proportion who responded that they had engaged in binge drinking
over the past month.
Why are the two sample proportions different?
Sample 1:
Sample 2:
(You must remember this notation!!)
wpget 127est.info
250 SamplePorportion p
0.508 0.468 statistic phat
justover 501PopulationPorportion p
included differentgroupsEstudents parameter
thus youwould expectdifferentsample
proportions

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

page 2
STA 205 Notes Buckley Fall 2018
What exactly is a sampling distribution and why is it important?
Example: According to a 2005 newspaper report about financial aid for college students, 75% of all full-time degree-
seeking students receive some form of financial aid. Given the recent financial crisis, an economist conjectures that the
percentage receiving some form of financial aid has increased. In order to test his conjecture, he plans to sample 265 full-
time degree-seeking students to determine the proportion that receive financial aid.
Two numbers are given in the example. Assign the appropriate notation (based on the previous page) to these values.
What is the conjecture that the economist is trying to find support for?
Suppose he takes a sample of 265 college students. Which would give more support to his conjecture â€“ finding that 204
Instead of taking a single sample of 265 students, suppose that 1000 different samples of 265 students were taken. A
sample proportion from each sample was computed and summarized in the graph below.
What seems familiar about the shape of this graph?
describes how the value or astatisticLF
Changes from sample to sample we want to use asample
im
eased runts
The
j
bellcurve
Looks like abell
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