Question

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350.To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypotheses are _________.

Answer 1

Null hypothesis:
`\mu \geq 800`

Alternative hypothesis:
`\mu <800`

Explanation:

For this case we define the random variable of interest X as the number of customers in a day. We are interested in the average number of customers visiting the dealership
`\mu` and we want to test if determine whether there has been a decrease in the average number of customers visiting the dealership daily.

From the info we know that the mean historical value for the average of customers per day is 800 so then that would be the alternative hypothesis since that's what we are trying to proof. And the complement rule would represent the null hypothesis.

Based on this the best system of hypothesis for this case are:

Null hypothesis:
`\mu \geq 800`

Alternative hypothesis:
`\mu <800`

The info given for this case:

`\bar X =750` represent the sample mean

`\sigma =350` represent the population deviation

n =100 represent the sample size

And in order to check the hypothesis we can use a z test for the mean.

Answer 2

H0: μ = 800

Ha: μ < 800

Explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Let μ represent the average number of customers visiting the dealership per day

The null hypothesis is that the average number of customers visiting the dealership per day is equal to 800

H0: μ = 800

The alternative hypothesis is that the average number of customers visiting the dealership per day is less than 800

Ha: μ < 800