After the opening of a new store in a city district, experts believed that the average price of a number of marketable goods would decrease. To check if this is the case, a researcher collected data from 23 district shops. The researcher conducts a signed-rank sum test and obtains, that the signed-rank statistic is 88. Assuming that the sample is large enough, make a conclusion about the probability of a decrease in the price.
A) The normal approximation of this study gives z = 1.34 and the probability that the price has not decreased is about P = 0.0901.
B) The normal approximation of this study gives z = 1.34 and the probability that the price has not decreased is about P = 0.9099.
C) The normal approximation of this study gives z = 0.05 and the probability that the price has not decreased is about P = 0.4801.
D) The normal approximation of this study gives z = 0.05 and the probability that the price has not decreased is about P = 0.5199.

Question

Quizplus · Accepted Answer

Since the sample size is greater than 20, we can use the normal approximation to the signed-rank test.

The signed-rank statistic is 88.

The corresponding z-score is:

z = (88 - 138)/15.492 = -3.2181

Looking at the standard normal table, the probability of getting a z-score of -3.2181 or lower is approximately 0.00065. Therefore, the probability of getting a z-score of 1.34 or higher is approximately:

P(z ≥ 1.34) ≈ 1 - 0.0901 ≈ 0.9099

So the best choice is A, which states that the probability of the price not decreasing is about 0.0901, which is the complement of the probability of getting a z-score of 1.34 or higher.

After the Opening of a New Store in a City