Question

Perform the following tests answering each part. Assume random samples taken from populations that are normally distributed. A supplier of cards claims that no more than 1% are defective. In a random sample of 500 cards, it is found that 2% are defective, but the supplier claims it's only a sample fluctuation. At a 0.01 significant level, test the claim.

1.What is the Claim in symbolic Format?

2.What is the Rest in symbolic Format?

3.What is the H₀?

4.What is the H₁?

5.What is α?

6.What type of tail test is this?

7.What is the test statistic?

8.What is the value of the test statistic?

9.What is the p-value?

Answer 1

claim: p <= 0.01
rest: p > 0.01

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p <= 0.01
Alternative Hypothesis, Ha: p > 0.01

This is right tailed test, for α = 0.01

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.02 - 0.01)/sqrt(0.01*(1-0.01)/500)
z = 2.25

P-value Approach
P-value = 0.0122

As P-value >= 0.01, fail to reject null hypothesis.