Question

Managers at a local phone service wireless retail center have a goal that 75​% of the​ center's customers will have to wait less than five minutes for service. The data below shows the wait times of a random sample of 25 customers in minutes. Does this sample provide evidence that​ management's goal is being​ achieved?

"The random sample of wait times."

41	5.7	2.3	10.3	3.4
3.8	0.4	7.4	4.4	5.1
4.7	2.6	3.7	9.6	6.6
5.4	4.7	0.3	2.9	5.7
5.1	3.6	2.2	2.2	4.6

Does this sample provide evidence that​ management's goal is being​ achieved? ​(Round to four decimal places as​ needed.)

A) No, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is_______which is less than 0.05.

B) Yes, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is_______ which is more than 0.05

C) Yes, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is _______ which is less than 0.05

D) No, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is _______ which is more than 0.05.

Answer 1

A) No, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is 0.0416 which is less than 0.05.

here we want to test

null hypothesis H0:P>=0.75 and

alternate hypothesis Ha:P<0.75

here n=25 and there are 15 customers who waited less than 5 minutes

so =x/n=15/25=0.6 and SE()=sqrt(P(1-P)/n)=sqrt(0.75*(1-0.75)/25)=0.0866

we use z-test and z=(-P)/SE()=(0.6-0.75)/0.0866=-1.7321

p-value=P(Z<-1.7321)=0.0416 ( using ms-excel(-1.7321))

since p-value is less than typical level of significance alpha=0.05, so we fail to accept H0 and conclude that sample provide evidence that​ management's goal didnot achieve.

right choice is A) No, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is_______which is less than 0.05.