Question

A successful waffle-man has recently developed a new recipe for waffles. To test the popularity of this new waffle compared to two other tried-and-true types of waffles, our friend the waffle-man randomly selected 180 lucky customers to vote on which of the three waffle types they liked best. Exactly 35% of these customers (or 63 in total) voted in favor of the new waffle. If all waffles were equally tasty, then the waffle-man knows to expect that each waffle would receive around 1/3 of the votes (so around 60 votes per waffle). Are 63 votes for the new waffle enough to conclude that significantly more customers like it compared to the others? Luckily, our friend the waffle-man triple-majored in waffles, statistics, and clinical neurophysiology and knows how to objectively answer this question. He conducts a hypothesis test for proportions, H0:p=0.333 , Ha:p>0.333 with a sample proportion of 63/180. In carrying out this test, what null distribution should she use? In other words, what is the distribution of the test statistic assuming the null hypothesis is true? (Be sure to use at least four decimal places in your calculations.) Select one: a. A normal distribution centered at 1/3 with a standard deviation of about 0.0351. b. A normal distribution centered at 0.333 with standard deviation of about 0.0356 c. A normal distribution centered at 0.35 with standard deviation of about 0.0356. d. A normal distribution centered at 0.35 with standard deviation of about 0.0351. e. We cannot use a null distribution in this problem because the population is not normally distributed.

Answer 1

Correct option:

c.     A normal Distribution centered at 0.35 with standard deviation of about 0.0351.

Sample Size = n = 180

Sample proportion = = 63/180 = 0.35

=1 - 0.35 = 0.65

SE =