FIND P VALUE QUESTION -- Resistors labeled as 100 are purchased from two differe
ID: 3310477 • Letter: F
Question
FIND P VALUE QUESTION -- Resistors labeled as 100 are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made.
Find the P-value. Round the answer to four decimal places.
Explanation / Answer
This is a difference in the proportion test
lets calculate this step by step
p1 = 149/180 = 0.827
n1 = 180
p2 = 233/270 = 0.862
n2 = 270
Since the null hypothesis states that P1=P2, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.
p = (p1 * n1 + p2 * n2) / (n1 + n2)
where p1 is the sample proportion from population 1, p2 is the sample proportion from population 2, n1 is the size of sample 1, and n2 is the size of sample 2.
p = (p1 * n1 + p2 * n2) / (n1 + n2)
= (0.827*180 + 0.862*270)/(180+270)
= 0.848
Compute the standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
where p is the pooled sample proportion, n1 is the size of sample 1, and n2 is the size of sample 2.
sqrt( 0.848 * ( 1 - 0.848 ) * [ (1/180) + (1/270) ] )
= 0.0345
The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
where p1 is the proportion from sample 1, p2 is the proportion from sample 2, and SE is the standard error of the sampling distribution.
Z = (0.827 - 0.862)/0.0345
= -1.014
for greater we calculate the p value as
P ( Z<1.014 )=1P ( Z<1.014 )=10.8438=0.1562
as the p value is not less than 0.05 , hence we fail to reject the null hypothesis
The data do not demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification
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