Question

A sample of 1100 computer chips revealed that 48% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 51% of the chips fail in the first 1000 hours of their use. Is there a sufficient evidence at the 0.05 level to support the companies claim? state the null and alternative hypothesis for the above scenarios?

H0=

Ha=

Answer 1

Solution :

Given that,

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.51

Ha: p 0.51

Test statistics

z = ( - ) / *(1-) / n

= ( 0.51 - 0.48) / (0.48*0.52) / 1100

= 1.992

P_value = 2*P(Z > z )

= 2 * ( 1 - P(Z < 1.992 ))

= 2 * 0.0232

= 0.0464

The p-value is p = 0.0464, and since p = 0.0464 < 0.05, it is concluded that the null hypothesis is rejected.

There is a sufficient evidence at the 0.05 level to support the companies claim.