Question

For problems 5 and 6 a washing machine maker claims that 90% of the machines it has sold are still working. A random survey of 100 of the maker's washing machines reveal that 85 of them are still working. Does this contradict the maker's claim at a 5% level of significance? Use the P value to determine this. 5. Give the null hypothesis and the alternative hypothesis used here. 6. Give the P-value and the conclusion to the question from this P-value.

Answer 1

5. Here claim is that p=0.90

So hypothesis is $H_0:p=0.90$ vs $H_1:p\neq0.90$

6. $\widehat{p}=\frac{85}{100}=0.85$

So test statistics is $z=\frac{\widehat{p}-p}{\sqrt{\frac{pq}{n}}}=\frac{0.85-0.90}{\sqrt{\frac{0.90*0.10}{100}}}=-1.67$

So P value is $2*P(z<-1.67)=2*0.0475=0.095$

As P value is greater than alpha=0.05, we fail to reject the null hypothesis

So the claim is correct