HW Problem 40. (5 pts) Geauga Park District claims that 10% of Geauga County res

Question

HW Problem 40. (5 pts) Geauga Park District claims that 10% of Geauga County residents have used the Maple Highlands bike trail at least once since it opened. A local tax payer believes this number is too high and that the proportion of Geauga County residents who have used the Maple Highlands trail is less than 10%. 300 Geauga County residents are randomly sampled and 24 indicate they have used the trail at least once. At the .05 level of significance, test to see if there is enough evidence to conclude that the taxpayer is correct in his belief that fewer than 10% of Geauga County residents have used the Maple Highlands trail at least once. List and clearly label all eight steps.

Explanation / Answer

1)here null hypothesis:Ho: p=0.1

2)alternate hypothesis:Ha: p<0.1

3) level of significance =0.05

4) test : one sample proprotion test ; test statistic =z

5)Deciison rule

for 0.05 level and left tailed test crtiical value of z =-1.6449

rejection region :reject Ho if test statistic z<-1.6449

6) for n=300 ; std errror =(p(1-p)/n)1/2 =0.0173

sample proportion phat =24/300 =0.08

hence test statistic z=(phat-p)/std error =(0.08-0.10)/0.0173 =-1.1547

7) Deciison :as test statistic is not in crtiical region we can not reject null hypothesis

8) Conclusion:there is not sufficient evidence to conclude that  the taxpayer is correct in his belief that fewer than 10% of Geauga County residents have used the Maple Highlands trail at least once.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

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