Exhibit 20.11.A wine magazine wants to know if chefs can tell the difference between duck liver pate and wet dog food.Eighteen chefs were asked to rate both the pate and dog food on a scale from 1 to 5,with 1 corresponding to "inedible" and 5 to "very tasty".The results are shown in the following table. Refer to Exhibit 20.11.Assuming has the standard normal distribution,the p-value for the test is:
A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question

Exhibit 20.11.A wine magazine wants to know if chefs can tell the difference between duck liver pate and wet dog food.Eighteen chefs were asked to rate both the pate and dog food on a scale from 1 to 5,with 1 corresponding to "inedible" and 5 to "very tasty".The results are shown in the following table.  Refer to Exhibit 20.11.Assuming  has the standard normal distribution,the p-value for the test is:
A)Less than 0.01 
B)Between 0.01 and 0.05 
C)Between 0.05 and 0.10 
D)Greater than 0.10

Quizplus · Accepted Answer

The null hypothesis is that there is no difference between the ratings of duck liver pate and wet dog food. The alternative hypothesis is that there is a difference between the two ratings. A two-sample t-test is appropriate for this situation since we are comparing two independent samples (the pate ratings and the dog food ratings) and assuming equal variances. The test statistic is -3.67 and the p-value is less than 0.01. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the ratings of duck liver pate and wet dog food.