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Q: Sales - reduction in Price ( Answered,   0 Comments )
Subject: Sales - reduction in Price
Category: Business and Money
Asked by: waterballoon1-ga
List Price: $45.00
Posted: 28 Aug 2005 22:05 PDT
Expires: 27 Sep 2005 22:05 PDT
Question ID: 561642
An owner wanted to know if a 10% reduction in price would affect the
number of sales.  She documented the following random weekly sales
numbers of his product:

REGULAR PRICE	138	121	88	115	141	125	96	
REDUCED PRICE	128	134	152	135	114	106	112	120

Perform the appropriate hypothesis test and calculate the following:

1.	H0.
2.	H1.
3.	t Critical.
4.	t Calculated.
5.	Decision.
6.	Explanation of Decision
Subject: Re: Sales - reduction in Price
Answered By: omnivorous-ga on 29 Aug 2005 10:37 PDT
Waterballoon1 ?

1.  Anything in that range that matches our existing condition for
sales is the hypothesis H0 (also called the null hypothesis) ? that
the reduced sales price doesn?t increase sales.

2. Only those values outside the range would support hypothesis H1 ? 
the alternate hypothesis ? that reducing prices by 10% increases

Statistics Glossary
?Hypothesis Testing?

To calculate the values, we?ll need the mean of both populations:
Mean = 117.7
S.D. = 7.53

Mean = 125.1
S.D. = 5.34

2. What?s the t-critical value?  That depends on the confidence level
that we?re trying to get.  We?re dealing with a single-tailed
T-distribution and 8 samples ? so we use 7 degrees of freedom (it?s
always N-1 for the student T-distribution) and at the following levels
the critical values are determined from the following table:

Statsoft Electronic Textbook
?Student?s T Table? (2003)

Critical T-values (single-tailed distribution):

90% confidence: 1.415
95% confidence: 1.895
99% confidence:  2.998

3.  You?ll accept the H0 hypothesis based on whether or not the same
falls in the range of:
mean + T-crtical * SD
?Statements of probability and confidence intervals? (undated)

Calculated T-values
90% confidence: 1.415 * 7.53 = 10.66
95% confidence: 1.895 * 7.53 = 14.27
99% confidence:  2.998 * 7.53 = 22.57

5.	Thus, we?re 90% confident that any results with 117.7 + 10.66 =
128.36 are within the expectations for REGULAR price.  So, we accept
H0 because our sample mean was 125.1 units of sales.

6.	We?ve tested the hypothesis at a moderately high level of
confidence ? the 90% level.  If we want to be more critical we can
look at a higher confidence level ? but it will merely expand the
range and lead to H0 being accepted.

Only weakening the hypothesis testing to a 75% confidence level
(T-critical = 0.711), do we end up with values that suggest reducing

75% confidence: 5.35 

REGULAR price @ 75% confidence level = 117.7 + 5.35 = 123.05 == > accept H1

However, a 75% confidence level is generally considered too low in
most research to result in acceptance of the alternate hypothesis.

In addition, more statistical sampling of the REDUCED price scenario
will not change confidence levels -- as an infinite number of samples
still puts REDUCED price inside H0 for 90-99% confidence levels.

Google search strategy
t-distribution + critical
t-distribution + ?hypothesis testing?

Best regards,

There are no comments at this time.

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