Hi all,
I have a hypothesis test of proportion question without using R. I hope you
could help to answer my question.
Here is the statement.
*********************
Preliminary data from a feasibility study showed a potential failure level
of 1%. A sample size was calculated to detect a potential shift from this 1%
level to a 2.5%, at an alpha level of 0.025 and beta of 0.1. The sample size
required is therefore 756 per condition. Acceptance criteria is 14 failures
or less per condition.
Power anlaysis of one proportion:
Numeric Results for testing H0: P=P0 versus H1: P>P0
Test Statistics: Exact Test
Power N Proportion Given H0 Proportion Given H1 Target
Alpha Actual Alpha Beta
(P0) (P1)
0.9007 756 0.01 0.025
0.025 0.0223 0.0993
The acceptance criterion is based on a sample size calculation to compare
two proportions (alpha and beta set at given levels). With 756 samples you
could find up to 14 failures and be able to claim that the process didn’t
move from a 1% to a 2.5% defect level. The calculations are based on the
binomial distribution.
*********************
My question is :---- Why the acceptance criteria is 14 or less failure per
condition???
I have made a table calculating the probability of each failure,
Number of failure Sample proportion Binomial Probability Cumulative
Probability 0 0 0.000501426 0.00050143 1 0.001322751 0.003829074 0.0043305 2
0.002645503 0.014600761 0.01893126 3 0.003968254 0.037067251 0.05599851 4
0.005291005 0.070483939 0.12648245 5 0.006613757 0.10707863 0.23356108 6
0.007936508 0.135380558 0.36894164 7 0.009259259 0.146515755 0.51545739 8
0.010582011 0.138560985 0.65401838 9 0.011904762 0.116322803 0.77034118 10
0.013227513 0.087770842 0.85811202 11 0.014550265 0.060125848 0.91823787 12
0.015873016 0.037705182 0.95594305 13 0.017195767 0.021796935 0.97773999 14
0.018518519 0.011684793 0.98942478 15 0.01984127 0.005838462 0.99526324 16
0.021164021 0.00273125 0.99799449 17 0.022486772 0.001200906 0.9991954
As the alpha = 0.025, isn't the acceptance region should be less than
1-0.025 = 0.975? isn't the acceptance criteria be 12 or less failure
according to the table above?
I hope you an answer my question. Thanks!!
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