Question

The owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. Specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. Chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. She randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. What are the null and alternative hypotheses for this hypothesis test?

1.{H0:p=0.63Ha:p>0.63
2.{H0:p=0.63Ha:p<0.63
3.{H0:p≠0.63Ha:p=0.63
4.{H0:p=0.63Ha:p≠0.63

Answer 1

For this case we want to test if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014 or if the proportion differs from 0.63 (alternative hypothesis) and the complement would be the null hypothesis. So then the system of hypothesis are:

Null Hypothesis:
`p=0.63`

Alternative hypothesis:
`p \\eq 0.63`

And the best option would be:

4.{H0:p=0.63Ha:p≠0.63

Explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014 or if the proportion differs from 0.63 (alternative hypothesis) and the complement would be the null hypothesis. So then the system of hypothesis are:

Null Hypothesis:
`p=0.63`

Alternative hypothesis:
`p \\eq 0.63`

And the best option would be:

4.{H0:p=0.63Ha:p≠0.63