DSC 211
CLASS NOTES 1-2
Last Topic of DSC 210 – Statistical Estimation:
Using sample results, answer the question,
“What is the value of the mean of the whole population & how precise (margin of error) is the
estimate?”
For example, “From the sample what is the best estimate of average expenditure (
μ
)
including a 95% confidence possible error (MOE)?”
First Topic of DSC 211 – Hypothesis/Claim Testing
:
Using sample results, answer the question
,
“Can we reject a claim (i.e., conclude the counter claim) about the value of the mean of the
whole population?”
For example, “Based on the sample, can we conclude that the average
expenditure of all customers is > $100? (same as: Can we reject the claim that average is <=
$100?)”
THERE WILL BE 6 STEPS TO THIS “HYPOTHESIS TESTING” PROCEDURE:
Consider the following situation:
Let’s use our BFDA scheme.
BUSINESS ISSUE
–
All the current customers for our upscale line of products and their
income.
(We have assumed, based on a study last year, recently that their average income level
is $80,000. Before we make some marketing decisions, we decide to conduct another study
because we think the average income may have increased)
BUSINESS QUESTION
of this study is the following:
Can we conclude from this study
(i.e., from the sample data) that the average income of all our customers is now above
$80,000?
(Note that this business question is about mu, the mean income of all members of the
population.
This is the same as: Can we reject
the claim that the average is <= $80,000?)
DATA
Income data from a random sample of 36 customers: suppose the sample mean (x-bar) =
$83,500.
Also, we believe we know the standard deviation of all
customer incomes (sigma,
population stdev):
$10,000.
ANALYSIS: 6 STEPS OF ANY HYPOTHESIS TEST
EXAMPLE
1.
Hypotheses:
State the two hypotheses.
Ho, the null hypothesis, and
Ho:
mu <= 80 (in $1000s)
Ha, the alternative hypothesis (research hypothesis)
Ha:
mu > 80
Note:
Ha will always be the restatement of the business question.
Note:
If Ho is not true, then the answer to the business question is YES.
The hypothesis
test is structured to see if the sample allows us to REJECT Ho.
2. Test Statistic:
Identify (1) what we calculate from
(1)
Test statistic =
x-bar.
the sample results – the sample statistic
(2)
Identify by name
(we will calculate its value in Step 5.
)
will be Normal with mean =80
Also identify (2) the sampling distribution (If Ho is true)
of the test statistic.
Note: In this case, the Central Limit Theorem says that x-bars will be Normal and we
calculate the StDev of x-bar (or StdErr) = sigma/n^.5 = 10/36^.5 = 1.67.
3. Significance Level: