I need help with this question number 22 parts a,b&c please! Metropolitan Bus Co
ID: 3232425 • Letter: I
Question
I need help with this question number 22 parts a,b&c please! Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is than 5 minutes. A random sample of 20 waiting times has a mean of 3.7 minutes with a standard deviation of 2.1 minutes. At a = 0.01, test the bus company's claim. Assume the distribution is normally distributed. (Make sure you show all steps, including your interpretation.) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day where the mean is 60 tickets with a standard deviation of 13 tickets. At a = 0.01, test the group's claim. (Make sure you show all steps, including your interpretation.) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80hours. If a = 0.05, test the manufacturer's claim using confidence intervals. (Make sure you show all steps, including your interpretation.)Explanation / Answer
22) null hypothesis: mean=5
alternate hypothesis: mean<5
for std error =std deviation/(n)1/2 =0.47
hence test stat t=(X-mean)/std error =(3.7-5)/0.47=-2.7685
as for above p value =0.0061 which is less then 0.01 level we reject null hypothesis and conclude that claim was right
22 b) null hypothesis: mean =60
alternate hypothesis:mean >60
as X=mean
hence test stat =0
for above p value -0.5
as p vlaue is higher then 0.01 level we can not accept the claim
22 c)for std error =std deviation/(n)1/2 =16
for 24 degree of freedom and 95% CI ; t=2.0639
hence confidence interval =sample mean -/+t*Std error =946.9776 ; 1013.022
as above interval contain 1000 hours as probable value we can not reject null hypothesis that mean life is 1000 Hours