Question

The median rental for a three bedroom bungalow is 2400 per week. A random sample or 300 units showed 10 for exactly 2400 per week and 170 rented for more than 2400.   Can we conclude that the median rental is more than 2400 (at a 0.05 level)

1. State Ho and H1
2. Give a decision rule
3. Arrive at a decision

Answer 1

a) H₀: median is equal to 2400

H₁: median is greater than 2400

b)

Step 1: Find the obtained frequency (of). There are 120 (300-10-170) units with rents below the median (the median is 2400), and 170 above.
of = 120 and 170.

Step 2: Find the expected frequency (ef). The total number of data points—units—is 300. If 2400 was a true median, we’d expect to have 150 units with rents over 2400 and 150 units with rents below it.
ef = 150.

Step 4: Calculate the chi-square:

Χ² = Σ [(of – ef)²/ef].

This is:
(120 – 150)²/150 + (170 – 150)²/150

= 8.666

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.

Decision rule & Decision:

Since our Χ² value of 8.666 is greater than the critical Χ² value of 3.84, we reject the null hypothesis (i.e. we accept the alternative hypothesis) —i.e we accept that the median rental is more than 2400. If the Χ² value we calculated from our data had been less than the critical Χ² value, we would be able to accept the null hypothesis.