Question

A supplier of digital memory cards claims that less than 1% of the cards are defective. In a random sample of 600 memory cards, it is found that 2% 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 less than 1% are defective.

Answer 1

The supplier claims that defective cards are less than 1%. This is the claim to be testest so this is null hypothesis. Because we would reject or not reject this claim.

Since we are testing for the proportions and n > 30, we will use the z-test.

'p' being the population proportion of being defective

Null: p <= 1%

Alternative: p > 1%

= 2% n = 600 = 1%

Test Stat :

p-value =P( Z > |Test Stat|)

=1 - P(Z < |Test Stat|) .........................using normal probability tables

Sample p	2%
n	600
Null p	1%
Test Stat	1.7496
p-value	0.0401		P(z<1.75)=	0.9599
Since p-vaue > 0.01	level of significance=0.01
Decision	Do not reject the null hypo
Conclusion	There is insufficient evidence to reject supplier's claim.