Question

A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 185 items, the defect rate is 5.9%. The manager claims that this is due only to the sample fluctuation (random sampling variation) and that the process is not really out of control.

a. Test his claim at the 0.01 level of significance. Use both the RR and P-Value (Methods).

b. Assume that in fact the proportion of defects really is 0.009. Was an error committed? If so, what type?

Answer 1

a)

Ho: p <= 0.03

Ha: p > 0.03

TS= (p^ - p)/sqrt(pq/n)

= (0.059 - 0.03)/sqrt(0.03*0.97/185)

= 2.31226

at 0.01 alpha

critical value is 2.327

since TS < critical value

we fail to reject the null hypothesis

using p-value

p-value = P(Z > TS) = P(Z > 2.31226) = 0.0104

since p-value > alpha

we fail to reject the null hypothesis

we conclude that there is not sufficient evidence to reject the claim

b)

since p = 0.009 hence null hypothesis is true

and we fail to reject the null hypothesis

hence there have no error