5. The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one month to determine if the market share increases with new labels.
a.Write the company’s null and alternative hypotheses
b.In this context describe a Type I error and the impact such an error would have on the company.
c.In this context, describe a Type II error and the impact such an error would have on the company.
A sample has M = 72 and s = 4. In this sample, what is the X value corresponding to z = –2.00?
Substitute the values given if you are expected to solve for x in this formula:
z = (x - mean)/sd -->sd = standard deviation.
-2.00 = (x - 72)/4
Solve for x.
Here's a few hints:
Null hypothesis:
Population proportion is equal to some value.
Alternative hypothesis:
Population proportion is greater than some value. (The problem is asking if the market share increases.)
Type I errors result when you reject the null and it's true. Type II errors result when you accept the null and it's false.
See if you can go from here.
A sample has M=72 and s=4. In this sample, what is the X value corresponding to
z = -2?
is the answerposted for this?
a. The company's null hypothesis could be that the new marketing campaign and labeling will not significantly increase the market share of Crest toothpaste. The alternative hypothesis could be that the new marketing campaign and labeling will significantly increase the market share of Crest toothpaste.
b. In statistics, a Type I error refers to rejecting the null hypothesis when it is actually true. In the context of this scenario, a Type I error would occur if the company invests in the new marketing campaign and labeling based on the product trials, but there is actually no significant increase in the market share of Crest toothpaste. This would lead to wasted resources and potentially financial losses for the company.
c. On the other hand, a Type II error refers to accepting the null hypothesis when it is actually false. In this scenario, a Type II error would occur if the company decides not to invest in the new marketing campaign and labeling based on the product trials, but there is actually a significant increase in the market share of Crest toothpaste. This would result in missed opportunities for growth and potentially losing market share to competitors.