Question

"A supplier of digital memory cards claims that no more than 1% of the cards are defective. In a random sample of 600 memory cards, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective."

Answer 1

Both the values fall in the critical region so we reject H0: p ≤ 0.01 and conclude that the results are significantly different from chance identification and it is not a sample fluctuation.

Explanation:

1) Formulate the hypothesis

H0: p ≤ 0.01 against the claim Ha: p > 0.01

2) Choose the significance level ∝= 0.01

3) The test statistics under H0 is

z= x -np /√npq ( without continuity correction)

z= x ± 1/2 -np /√npq ( with continuity correction)

4) the critical region is z> ±2.33 because the alternate hypothesis is stated on greater than basis.

5)Computations:

Z= x -np /√npq ( without continuity correction)

Z= 6- 600( 0.03)/√ 600( 0.03)(0.97)

z= - 2.82 ( without continuity correction)

z= x ± 1/2 -np /√npq ( with continuity correction)

Z= (6-0.5)- 600( 0.03)/√ 600( 0.03)(0.97)

z= -12.5/4.1785

z= -0.29915 ( with continuity correction)

6) Both the values fall in the critical region so we reject H0: p ≤ 0.01 and conclude that the results are significantly different from chance identification and it is not a sample fluctuation.