A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink.In order to determine which one to promote,they took a sample of 80 patrons and asked them to choose which they preferred.The one that is significantly preferred over the other (at a .05 level of significance)will be promoted.It is expected that an equal number of patrons will choose each flavor.Based on the observed frequencies given below,what is the decision for this test?
A)Promote the swizzleberry swirl flavored drink.
B)Promote the creamsicle flavored drink.
C)Do not promote any flavored drinks.
D)There is not enough information to answer this question.

Question

A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink.In order to determine which one to promote,they took a sample of 80 patrons and asked them to choose which they preferred.The one that is significantly preferred over the other (at a .05 level of significance)will be promoted.It is expected that an equal number of patrons will choose each flavor.Based on the observed frequencies given below,what is the decision for this test? 
A)Promote the swizzleberry swirl flavored drink. 
B)Promote the creamsicle flavored drink. 
C)Do not promote any flavored drinks. 
D)There is not enough information to answer this question.

Quizplus · Accepted Answer

We need to perform a chi-squared goodness of fit test to determine if there is a significant difference between the number of patrons who prefer the swizzleberry swirl and the number who prefer the creamsicle flavored drink. The expected frequency for each flavor is 40 (an equal number of patrons is expected to choose each flavor). The observed frequencies for each flavor are:
Swizzleberry swirl: 28
Creamsicle: 52
We can calculate the chi-squared statistic as follows:
((28-40)^2/40) + ((52-40)^2/40) = 6.4
Using a chi-squared distribution table with 1 degree of freedom and a significance level of .05, we find that the critical value is 3.84. Since our calculated chi-squared value (6.4) is greater than the critical value (3.84), we reject the null hypothesis (that there is no significant difference between the number of patrons who prefer each flavor). Therefore, we can conclude that the creamsicle flavored drink is significantly preferred over the swizzleberry swirl and should be promoted.

A Local Ice Cream Shop Wants to See If They