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Question: A manufacturer reported that 95% of electronic components manufactured by them are free from defects. From a random sample of 80 components, 5 had defects. Find the p-value for the test. Is there enough evidence to reject the manufacturer's report at α = 0.01?


A ) 0.305; yes
B ) 0.61; yes
C ) 0.305; no
D ) 0.61; no

Steps to derive

1 H0: p = 0.95 and H1: p ≠ 0.95
 [Null and Alternate Hypotheses.]

2 Sample proportion, pˆ = 7580 = 0.9375

3 The test value, z = pˆ-pp(1-p)n, where p is the population proportion and n the sample size.

4 z = 0.9375-0.95(0.95)(0.05)80 = - 0.51
 [Substitute the values and simplify.]

5 Area under the standard normal distribution curve for z = - 0.51 is 0.1950. That is P(- 0.51 < z < 0) = 0.1950
 [Use the standard normal distribution table.]

6 P-value for a two tailed test = 2 × P(z < - 0.51)
6 = 2(0.5000 - 0.1950) = 0.61

7 The P-value 0.61 > 0.01, do not reject the null hypothesis.

8 So, there is not enough evidence to reject the manufacturer's report that 95% of electronic components have no defects.



Hence the right answer is Option D

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