In The American Statistician (May 2001), the nonparametric sign test was used to analyze data on the quality of white shrimp. One measure of shrimp quality is cohesiveness. Since freshly caught shrimp are usually stored on ice, there is concern that cohesiveness will deteriorate after storage. For a sample of 20 newly caught white shrimp, cohesiveness was measured both before and after storage on ice for two weeks. The difference in the cohesiveness measurements (before minus after) was obtained for each shrimp. If storage has no effect on cohesiveness, the population median of the differences will be 0. If cohesiveness deteriorates after storage, the population median of the differences will be positive.
a. Set up the null and alternative hypotheses to test whether cohesiveness will deteriorate after storage.
b. In the sample of 20 shrimp, there were 13 positive differences. Use this value to find the p -value of the test.
c. Make the appropriate conclusion (in the words of the problem) if a = .05.