In a certain city, 45% of the households have no dog, 30% have one dog, 10% have two dogs, 10% have three dogs, and 5% have four dogs. The population median number of dogs is therefore 1.

In a sample of 100 households, 45 have 0 dogs, 30 have one dog, 10 have two dogs, 10 have three dogs, and 5 have four dogs. Note that the sample reflects the population perfectly. Consider the hypotheses H0: m = 1 versus H1: m < 1.

Compute the value of the test statistic for the sign test and show that H0 is rejected at the α = 0.05 level.

Exercise 19 demonstrates that the sign test will generally not work when the population is discrete.