6. A computer manufacturer ships laptop computers with the batteries fully charg

Question

6. A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 100 new model laptops to various company sites around the country. Of the 100 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that this model's rate is higher than the previous model? Test the hypothesis at = 0.025.

Explanation / Answer

here null hypothesis: Ho: p=0.85

alternate hypothesis: Ha: p>0.85

as n=100 ; np=85 and n(1-p) =15 ; both are greater then 10 therefore we can use normal approximation of binomial distribution and apply 1 sample z test for proportion

for 0.025 level and right tail test ; critical value of z =1.96

Decision rule: reject Ho if test statistic z>=1.96

std error of proportion =(p(1-p)/n)1/2 =(0.85*(1-0.85)/100)1/2 =0.0357

sample proportion p hat =96/100=0.96

therefore test statistic z=(phat-p)/std error =(0.96-0.85)/0.0357 =3.0806

as test statistic is higher then critical value ; we reject null hypothesis.

we have sufficient evidence at 0.025 level to conclude that this model's rate is higher then previous model

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.