The bottlers of Coke claim that less than 5 perc of 20 oz. bottles of contain to

Question

The bottlers of Coke claim that less than 5 perc of 20 oz. bottles of contain too much caffeine. Of 400 bottles sampled, 15 were found to have too much caffeine. a) Determine whether the sample size is large enough to assume the distribution of the sample proportion (i.e., p) is normally distributed b) Conduct a hypothesis test with a level of of determine whether the true proportion of bottles of Coke with too much is less the null hypothesis, the alternative hypothesis, than percent. Show p-value, and give an the test statistic, the rejection region, the appropriate conclusion.

(70 pt) The bottlers of Coke claim that less than 5 perc of 20 oz. bottles of contain too much caffeine. Of 400 bottles sampled, 15 were found to have too much caffeine. a) Determine whether the sample size is large enough to assume the distribution of the sample proportion (i.e., p) is normally distributed b) Conduct a hypothesis test with a level of of determine whether the true proportion of bottles of Coke with too much is less the null hypothesis, the alternative hypothesis, than percent. Show p-value, and give an the test statistic, the rejection region, the appropriate conclusion.

Explanation / Answer

We have to test the null hypothesis Ho:p=0.05 verssu the alternative Ha:p<0.05 , where p is the proportion of bottles that contains too much caffeine.

WE have number of successes (too much caffience)=15 and number of failures=400-15=385 both of which are greater than 5, so assumption of normality satisifed

Sample proportion phat=15/400=0.0375

Test statistci Z=(phat-0.05)/sqrt(0.05*(1-0.05)/n)

=(0.0375-0.05)/sqrt(0.05*(1-0.05)/400)

=-1.147

p-value=P(Z<-1.147) =0.1257 using excel function =normsdist(-1.147)

As p-value>0.05, we do not reject the null hypothesis and concldue that bottlers of Coke claim is not supported and so propotion is not signficantly loewer than 0.05

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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