Question

A paper company requires that the true median height of pine trees exceed 40 feet before they are harvested. A penalty is assigned if the median height is less than 40 feet. The management wants to avoid this penalty. A sample of 24 trees in one large plot is selected, and 7 of them are over 40 feet. Conduct the appropriate hypothesis test to determine if the median height of pine trees in the plot is less than 40 feet. The estimated median is 35 feet. Do not assume normality. Let a = 0.05.

Answer 1

NULL HYPOTHESIS H0: Median=40 feet

ALTERNATIVE HYPOTHESIS Ha: Median>40 feet

alpha=0.05

Step 2: Find the observed frequency (of). There are 17 trees below the median (the median is 40), and 7 above.
observed frequency = 7 and 24.

Step 3: Find the expected frequency (ef). The total number of trees 24. If 40 feet was a true median, we’d expect to have 12 trees over 40 feet and 12 below.
ef = 12.

Step 4: Calculate the chi-square:

Χ2 = Σ [(of – ef)2/ef].

This is:
(17 – 12)^2/12 + (7 – 12)^2/12

or 2.08+ 2.08 = 4.16

Step 5: Find the degrees of freedom. There are two observed frequencies (equal to two cells in a contingency table), so there is just one degree of freedom.

Step 6: Use a Chi-squared table to find the critical chi-square value
for 1 degree of freedom and an alpha level of 0.05 (α = 0.05). This equals 3.84

Step 7: Since Critical value of chi square is SMALLER than calculated value of chi square we Reject null hypothesis and conclude that the median height of trees are greater than 40 feet. .