• Data: Daily high temperature (degrees C) for 9 randomly selected days in September.

    31 32 20 36 23 24 27 28 30

  • Analysis: Wilcoxon signed rank test.

    H: = 27
    A: > 27

    T- = 14 T+ = 22

    The P-value is 0.320. Since the P-value is not small we cannot reject H. The median high temperature could be 27 degrees C.

  • Estimation of the median high temperature: Calculate the 45 Walsh averages. Put the Walsh averages in order from smallest to largest. The median, 23rd Walsh average in the ordered set, is an estimate of the median high temperature. This value is 28.

    For an approximate 95%confidence interval, go to Table G.

    For P=0.027, k=6. The interval that goes from the 7th ordered Walsh average to the 39th ordered Walsh average is a 94.6% confidence interval for the median high temperature, 24 to 31.5.

  • Using the Walsh averages to find the test statistic Cover up the column and row that correspond to the hypothesized median value of 27. T- equal to the number of Walsh averages less than 27 plus 1/2 times the number of Walsh averages equal to 27. T+ is equal to the number of Walsh averages greater than 27 plus 1/2 times the number of Walsh averages equal to 27.