STA 205 Lecture Notes - Lecture 8: Sampling Distribution, Standard Deviation, Flying Pig Marathon

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19 Dec 2018
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Packet 8: Sampling Distribution of the Sample Mean Textbook pages: 24 30; 701 704
After completing this material, you should be able to:
explain what the symbols
y
µ
and
y
σ
represent.
describe the sampling distribution of the sample mean by discussing its shape, mean, and standard deviation.
find probabilities associated with various sample means based on the sampling distribution.
make inferences from the probability and explain the reasoning.
A local pub is interested in learning more about their daily sales. In order to do this, daily sales (measured in dollars) from
the past two months are collected. A histogram and summary statistics are given below. Use these to fill in the description
of the distribution below include units with the values where appropriate.
The distribution of ______________________________________ has a shape
that is ________________________________. The average sales for these
_________ days is ________________________, and 50% of the time daily
sales are ______________________or less. The smallest sales amount was
___________________, while the largest was _____________________.
The middle 50% of daily sales fell between ______________________ and _______________________. According to
_____________________________ Rule, we expect daily sales to fall between ________________________ and
__________________________ (three standard deviations from the mean) ___________% of the time.
Let’s assume this is our population of sales values what happens if we start to take samples of size 14 from this population
of values?
Below is the sample which was taken the values selected in the sample
have been highlighted in pink on the original histogram.
Sample Sales:
2062
2142
2503
2566
2814
2827
3189
3446
3748
4908
5788
5816
6105
6799
What is the mean for this sample of 14 days?
If we took another sample of 14 days would we expect the same
mean?
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weekday
daily pub sales wknd
µHis same
1bimodal 2right foranytype
skewd
GO 3917.443 251 25 251,251
3611.45 TI
1210.50121 1068.2013
2853.55141 5318.05151
Chebyshev's 0
8454.3646 golor more
391744331311512.307
Hneg _O 619 478 8454.3646
if 14924542
5174113693.4854
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false to the
Fading
For All
If we take another sample
we get different sale amounts
thus we get adifferent
value of J
Asampling distribution describes
how astatistic changes in
value from sample to sample
The sample mean Tis a
statistic that summarizes
QUANTITATIVE data The
sampling distribution of g
describes what values of g
we expect igIFr sles
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page 2
STA 205 Notes Buckley Fall 2018
Recall: What is a sampling distribution and why is it important?
We need to understand how the samples vary. To do this, we need to describe the sampling distribution of the sample
mean. To do this, the following three characteristics must be addressed:
Example: Each of the following histograms represents a sampling distribution of the sample mean for various sample
sizes. Samples of size 5, 15, and 40 were taken from some population. Match each histogram to the appropriate sample
size.
Based on the sampling distributions shown, what is the (approximate) population mean? Explain.
The population from which these samples were taken must have had what shape? Explain.
sample size: ___________
sample size: ___________
sample size: ___________
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we expect to get from samples
Shape nsolr
mean it
standard donation to
ib pieris
n5n15 n40
formally distributed
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