Step 1 of 4: State the null and alternative hypotheses in terms of the expected proportion for each flavor.
Given the proportions observed in the normal sales distribution before the promotional campaign and the observed sales after the campaign, we need to establish hypotheses to test whether the campaign has significantly altered the proportions sold of each flavor.
The null hypothesis ([tex]\(H_0\)[/tex]) represents the expected distribution if the campaign had no effect, based on the historical proportions. The alternative hypothesis ([tex]\(H_a\)[/tex]) states that at least one of the proportions is different from what was expected after the campaign.
Null Hypothesis ([tex]\(H_0\)[/tex]):
- [tex]\(H_0: p_{SG} = 0.20\)[/tex]
- [tex]\(p_{CM} = 0.10\)[/tex]
- [tex]\(p_{T} = 0.20\)[/tex]
- [tex]\(p_{BBQ} = 0.20\)[/tex]
- [tex]\(p_{AZ} = 0.30\)[/tex]
Alternative Hypothesis ([tex]\(H_a\)[/tex]):
- There is a difference from the stated proportions (i.e., at least one [tex]\(p_i\)[/tex] is different).
We are now ready to proceed to the subsequent steps where we will calculate the test statistic, the expected frequencies, and determine whether to reject the null hypothesis based on the 0.01 level of significance.
