Given:
𝑥1 = 15
𝑛1 = 300
𝑥2 = 8
𝑛2 = 300
α = 0.05
The claim is either the null hypothesis or the alternative hypothesis. The null
hypothesis and the alternative hypothesis state the opposite of each other. The null
hypothesis needs to contain an equality.
𝐻0 : p1=p2
𝐻1 : p1 ≠ p2
The sample proportion is the number of successes divided by the sample size:
p1 =
p2 =
𝑝𝑝 =
𝑥1
𝑛1
𝑥2
𝑛2
𝑥1+ 𝑥2
𝑛1+ 𝑛2
=
=
=
15
300
8
300
≈ 0.05
≈ 0.0267
15+ 8
300+ 300
≈ 0.0383
Determine the value of the test statistic:
𝑝𝑝 =
𝑝1+ 𝑝2
1
1
√𝑝𝑝 (1−𝑝𝑝 ) √𝑛1+ 𝑛2
=
0.05−0.0267
1
1
≈ 1.49
√0.0383(1−0.0383) √300+ 300
The P-value is the probability of obtaining the value of the test statistic, or a value
more extreme, assuming that the null hypothesis is true. Determine the P-value
using table the normal probability table in the appendix:
P = P(Z<−1.49 or Z>1.49)
= 2P(Z<−1.49)
= 2(0.068112)
= 0.136224
If the P-value is smaller than the significance level, then reject the null hypothesis:
P=0.136224 > 0.05 ⇒ Fail to reject 𝐻0
There is not sufficient evidence to reject the claim that both machine product the
same fraction of defective parts.
Result:
P = 0.136224
There is not sufficient evidence to reject the claim that both machine product the
same fraction of defective parts.