Keystone Light Hypothesis Test Proposal

Keystone Light Hypothesis Test Proposal

Kathy Birchall, Anne Abbott, Andrea Abeita

February 11, 2004

Goal: All three members of our group are in the middle of their fourth year at Dartmouth College, and we are acutely aware of the idiosyncrasies surrounding the social scene on campus. As opposed to other colleges, Dartmouth’s nightlife is dominated not by bars or clubs, but instead by attending parties hosted by Greek houses. Our group is particularly interested in this aspect of Dartmouth because all three of us belong to sororities and actively socialize within the Greek system. In our time at Dartmouth, the College has forbidden the presence of kegs on campus, and therefore students have been forced to resort to the cheapest method, which seems to be Keystone Light. Houses hold meetings every Wednesday night and unless the house is on probation or forbidden to have alcohol on the premises, most meetings are accompanied by several 30-pack cases of Keystone Light (as opposed to any other type of beer.) Also, fraternities and sororities commonly play pong, which is a rendition of table tennis with this particular beer. Because we’ve noticed that Keystone Light seems to be the most prominent beer served at the Greek houses on campus, we are interested to see if the constant presence of this beer makes it more recognizable to senior student taste testers that belong to a Greek organization. We have designed the following hypothesis test to determine if Greek-affiliated Dartmouth seniors can recognize Keystone Light when compared to another type of beer.

Null Hypothesis: To articulate the null hypothesis will require us to determine whether a subject often drinks beer in Greek houses and whether they can tell a difference between the two samples of beer. In order to accomplish this, we will ask our Greek-affiliated senior subjects the below Question 1 and Question 2 first. If they answer yes to both these questions, we will continue and include them in our test.

Question 1: Do you often drink beer in Greek houses on campus?

If they answer yes to this question, we will continue with the test, and have them try both our samples of beer. If they answer no, they will not qualify to be in our survey.

Question 2: Can you detect a difference between these two beers?

If they answer yes to this question, we will continue and include them in our test. If they say no, they will not qualify to be in our test.

Note: We will refer to those who answer yes to both these questions as EDs (experienced drinkers.)

Null Hypothesis: EDs will be equally likely to chose Keystone Light as either beer sample tasted. (In other words, they will not be able to recognize Keystone Light as opposed to the other light beer sampled.)

Alternate Hypothesis: A majority of the Greek-affiliated seniors tested with be able to correctly identify the Keystone Light.

Parameter: Under the null hypothesis, the EDs that we have selected will be equally likely to chose either cup as Keystone Light. Hence, the null hypothesis is that ptrue=pnull=0.5. The alternative hypothesis is that ptrue > pnull = 0.5. Ideally, we would like to find over 80% of our sample able to successfully identify the Keystone Light sample.

Test Statistic: We are planning on testing 30 EDs, realizing that we will likely have to question more than 30 students in order to find 30 that qualify for our test. We will label these 30 EDs as N, and K will be the number of EDs that correctly identify the Keystone Light beer sample. Our test statistic will be P, which will equal K/N. Under the null hypothesis, P will equal 0.5, and will distributed as a normal binomial distribution curve.

Significance Level: Because we want our results to be statistically significant, we are going to chose a significance level of 0.05, meaning that we will only leave a five percent chance of an alpha error.

Critical Region: Since our alternative hypothesis states that ptrue > pnull, our test will be right sided. Consequently, to find the critical region, we will use z0 = 1.65, and we will reject the null hypothesis if P is greater than or equal to (pnull + z0 (sq.rt.( pnull(1- pnull)/N))), which is P’s critical region. If P is greater than or equal to this above value, pcrit is equal to that above value.

Power Hypothesis: We believe that 80% of our EDs will correctly identify Keystone Light over the other light beer. With the belief that ptrue = pnull = 0.8, we can compute the power of this test. Because N will be equal to 30, we will be able to use the normal approximation curve. Therefore, the area to the right of the standardized pcrit (whose formula can be viewed below) will be the probability that we correctly assumed our alternate hypothesis and ppower = ptrue.

The of getting a beta error is at most 1-power. In this test, a type 2 error correspondes to the chance that ptrue > 0.8.

Test Population: For our test, we are each responsible for finding 10 EDs by Saturday, February 14th. We hope that well over half of the EDs tested correctly identify the Keystone Light, and we are hoping that our ptrue proves our alternative hypothesis correct. Pcrit will equal 0.65 and the power will equal 0.98, considering that ppower = 0.8. All of this information depends on the fact that we will each find 10 EDs.

Equipment: Since we are finding 30 EDs, and each will require two cups per person, and we will test some people who do not qualify as EDs, we will buy 80 plastic cups. We will purchase a permanent marker to mark the cups “A” and “B” to ensure that the identities of the cups will remain constant. We will also buy a 30-pack of Keystone Light and a couple cases of Amstel Light. (Luckily, if we run out, Stinson’s is right around the corner.) We will also provide amble bottled water and Saltine crackers for EDs who request to cleanse their palettes in between sips. We are setting aside all afternoon on Saturday, February 14th, to conduct this survey.

Protocol: Anne will act as the pourer and she will be responsible for giving the sampler an identification number. She will mark the cups with this identification number and either “A” or “B.” Anne will then pour the beers into their respective cups. Anne will be the only one that knows the correct identity of the samples, and will privately record them in a data sheet, next to the sampler’s identification number. Andrea will act as the distributor. Once Anne gives her the word to come and collect the cups, Andrea will enter the pouring room and take the cups from Anne into the sampling room. Andrea will hand these cups to Kathy and return to the pouring room. Kathy will then give the cups to the sampler, only if she has answered yes to Question 1. Kathy will then instruct the sampler to taste both A and B, offering the bottled water and Saltines if the sampler would like. Kathy will then ask the sampler Question 2. If the sampler answers yes to question 2, the sampler turns into one of our EDs. Kathy will then ask this ED question 3, which is “Which of these cups contains Keystone Light?” Kathy will then record the letter, “A” or “B,” into her data sheet next to the subject’s identification number. (Both the identification number and the letter “A” or “B” will be marked on the cups in magic marker by Anne in the pouring room before the tasting occurs.)