A wine magazine wants to know if chefs can tell the difference between duck liver pâté and wet dog food.Eighteen chefs were asked to rate both the pâté 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. Assuming has the standard normal distribution,the value of the test statistic for the sign test is __________.
A) 3.767
B) -3.767
C) 0
D) None of these choices is correct.None of the above

Question

A wine magazine wants to know if chefs can tell the difference between duck liver pâté and wet dog food.Eighteen chefs were asked to rate both the pâté 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.  Assuming  has the standard normal distribution,the value of the test statistic for the sign test is __________.
A) 3.767 
B) -3.767 
C) 0 
D) None of these choices is correct.None of the above

Quizplus · Accepted Answer

To use the sign test, we need to calculate the differences between the ratings for each chef: pâté rating minus dog food rating. Then, we count the number of positive differences and the number of negative differences. In this case, we have 11 positive differences and 7 negative differences (ties are ignored). The null hypothesis is that the median difference is zero (i.e., the chefs cannot tell the difference between pâté and dog food), and the alternative hypothesis is that the median difference is not zero (i.e., the chefs can tell the difference).

We can use the sign test formula for the test statistic:

z = (P - n/2) / sqrt(n/4)

where P is the number of positive differences, n is the total number of differences, and sqrt is the square root. Plugging in the values, we get:

z = (11 - 18/2) / sqrt(18/4) = -3.767

Note that we use the one-tailed version of the formula because the alternative hypothesis is one-sided (not equal). Also, we round the result to three decimal places. The critical value for a two-sided test at alpha = 0.05 is +/-1.96. Since -3.767 < -1.96, we reject the null hypothesis and conclude that the chefs can tell the difference between pâté and dog food. The answer is B.

A Wine Magazine Wants to Know If Chefs Can Tell