The number of pairs of shoes owned by adult women is assumed

The number of pairs of shoes owned by adult women is assumed to follow a skewed distribution. A random sample of 10 women was taken and each woman was asked how many pairs of shoes she owned. Their responses were: 7 24 15 7 18 15 9 13 8 14

Using these date test the hypothesis that the median number of pairs of shoes owned by adult women is 12. Apply the sing test with a 5% level of significance.

Solution

Set Up Hypothesis
Null, Median = 12
Alternate, Median !=12
Test Statistic as follows
n= 10
Below =4, Above = 6, P = 0.7539
Median = 13.50
P-Value :Two Tailed : 0.7539
Hence Value of P0.05 < 0.7539,we fail to reject null hypothesis. Thus, there is sufficient evidence to
conclude that the median number of pairs of shoes owned by adult women is 12

Since, 0.7539> 0.05