A manufacturer claims that less than 4% of his produced items are defective. In a random sample of 300 items, 11 were defective. At α=0.05, test the manufacturer claim.
Claim
H0
Ha
Test Statistic=
p-value=
Result:
Solution :
This hypothesis test is a left tailed test .
The null and alternative hypothesis is
H0 : p = 0.04
Ha : p < 0.04
= x / n = 11 / 300 = 0.0367
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
= 0.0367 - 0.04 / [(0.04 * 0.96) / 300]
= -0.295
P-value = 0.3841
= 0.05
P-value >
Fail to reject the null hypothesis .
There is not sufficient evidence to claims that less than 4% of his produced items are defective .
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