EXAMPLE 2 Changing the data values to plus or minus signs

Suppose that we are interested in testing whether the population median number of hurricane-related deaths per year is less than 50.

  1. Write the null and alternative hypotheses for this test.
  2. Change each data value that is less than 50 to a minus sign (–), and change each data value that is greater than 50 to a plus sign (+). Ignore any data values that are equal to 50. The sample size is the total number of plus signs and minus signs.

Solution

  1. We may write the hypotheses as

    where represents the population median number of hurricane-related deaths per year.

    14-7

  2. As shown here, we have 7 minus signs and 1 plus sign, so that our sample size is .
Year 1959 1963 1974 1988 1999 2001 2005 2010
Deaths 24 11 1 9 19 24 1016 13
Sign – – – – – – + –