Question

Some boxes of a certain brand of breakfast cereal contain a card with an access code for a free month of a particular entertainment streaming service. The company that makes the cereal claims that the access code can be found in 20% of the boxes. However, based on their experiences consuming the cereal, a group of students believes that the proportion of boxes which contain access codes is less than 20%. The group of students purchases 40 boxes of cereal to investigate the company’s claim. (Assume that the 40 boxes purchased by the students are a random sample of all boxes of this particular cereal). Of those 40 boxes, 6 contained the access code. Based on this sample, is there support for the claim that the proportion of boxes with access codes is less than 0.2? Use an alpha of 0.1. Your answer should contain statements of the null and alternative hypotheses, appropriate and correct calculations, and an answer to the question in the context of the scenario.

Answer 1

Using the P-value approach: The p-value is p=0.2146, and since p = 0.2146 ≥ 0.10, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the

the proportion of boxes with access codes is less than 0.2 at the α=0.10 significance level.