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Q: 95% confidence level ( Answered,   0 Comments )
Subject: 95% confidence level
Category: Science > Math
Asked by: mutiny58-ga
List Price: $10.00
Posted: 06 Oct 2005 12:57 PDT
Expires: 05 Nov 2005 11:57 PST
Question ID: 577268
The McFaland Insurance Company claims department reports the mean cost
to process a claim is $60. An industry comparison showed this amount
to be larger than most other insurance companies, so they instituted
cost-cutting measures. To evaluate the effect of the cost-cutting
measures, the supervisor of the claims department selected a random
sample of 26 claims processed last month.
The sample information is reported below:
45	49	62	40	43	61
48	53	67	63	78	64
48	54	51	56	63	69
58	51	58	59	56	57
38	76
At 95% confidence level is it reasonable to conclude that mean cost to
process a claim is now less than $60...Why?
Subject: Re: 95% confidence level
Answered By: omnivorous-ga on 06 Oct 2005 14:05 PDT
Mutiny58 ?

1.  Anything in that range that matches our existing condition for
mean costs is the hypothesis H0 (also called the null hypothesis) ?
that the efforts DO NOT change costs.

2. Only those values outside the range would support hypothesis H1 ? 
the alternate hypothesis ? that mean costs are now lower.

Statistics Glossary
?Hypothesis Testing?

To calculate the values in the statistical range, we?ll need the mean
and standard deviation, easily done in Excel or many programmable
Mean = $56.42
S.D. = $10.04

3.  It is effective to use the Student?s T-distribution for small
sample sizes, as it provides a statistical significance related to the
sample size.  Our sample size is 26 ? but the Student?s T-distribution
uses ?degrees of freedom? ? which is N-1 or 25.

What?s the t-critical value?  That depends on the confidence level
that we?re trying to get ? and whether we?re dealing with a two-tailed
or one-tailed T-distribution.  Here it?s distributed about the mean,
so it?s two-tailed (sometimes samples can vary only one way).

The critical values are determined from the following table:

Surfstat Statistical Tables
 ?Student?s T Table? (1997)

95% confidence: 2.06

4.  You?ll accept the H0 hypothesis based on whether or not the same
falls in the range of:
mean +/- T-crtical * SD

In our case this is:

$56.04 +/- 2.06 * $10.04 = $34.58 to $76.72 

With $60 well within that range, there?s no statistical reason to
believe that cost-control efforts changed anything, so you?re accept
H0 ? no change.
?Statements of probability and confidence intervals? (undated)

5.	What can you do to enhance your conclusions?  You can expand your
sample size, though your critical T never drops below 1.96 ? and you?d
have to get a much tighter standard deviation to judge the
cost-control efforts to be effective.

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

Best regards,

There are no comments at this time.

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