Question

The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario? (Ch10)

A. H0: m =7.5 and H1:m ? 7.5

B. H0: m <=7.5 and H1:m > 7.5

C. H0: m >=7.5 and H1:m < 7.5

D. H0: m <7.5 and H1:m >=7.5

E. H0: m >7.5 and H1:m <= 7.5

Answer 1

Answer: C .
`H_0:\mu\geq7.5` and
`H_a:\mu<7.5`

Explanation:

Definition:

Null hypothesis
`(H_0)` is a statement about the population parameter according to the objective raised by the researcher . It contains '=' , '≤' and '≥' signs.

Alternative hypothesis
`(H_a)` is also a statement about the population parameter but against null hypothesis . It contains '≠' , '<' and '>' signs.

Let
`\mu` be the average customer waiting time for the population.

Given : The average customer waiting time at a fast food restaurant has been 7.5 minutes.

Objective of test : After using new system , the average customer waiting time is at least 7.5 or less than 7.5.

Then, the null and alternative hypothesis for this scenario will be :

`H_0:\mu\geq7.5`

`H_a:\mu<7.5`