Question

A machine need repair if it produces more than 10% defectives among large amount of products. We randomly sampled 100 items, and find that there are 8 defectives. We claim that, the repair of this machine is not needed. Note: You should use R code to express your results, and run R code on laptop.

a) Assuming α = 0.01, apply large sample hypothesis testing to test whether or not the evidence suports this claim.

b) Calculate the p-value. What is your conclusion, reject or not?

c) If, in the above question, we find only 2 defectives from 100 items, could you reject the claim based on the p-value at the level α = 0.01?

Answer 1

The R output is:

The R code is:

pcap = 8/100
p = 0.10
n = 100
se <- sqrt((p*(1 - p))/n)
z <- (pcap - p)/se
1 - pnorm(z)
pcap = 2/100
p = 0.10
n = 100
se <- sqrt((p*(1 - p))/n)
z <- (pcap - p)/se
1 - pnorm(z)

(a) The hypothesis being tested is:

H0: p = 0.10

Ha: p > 0.10

z = -0.67

(b) p-value = 0.7475075

Since the p-value (0.7475075) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the machine needs repair.

(c) The hypothesis being tested is:

H0: p = 0.10

Ha: p > 0.10

z = -2.67

p-value = 0.9961696

Since the p-value (0.9961696) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the machine needs repair.

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