Answer to Question #151357 in Statistics and Probability for Hay

Question

Question 2
A group of reputable housing firms in Ghana claim that the mean price of
residential homes before the change of government does not exceeds the
mean price after the new government in Ghana came to power. Tonaton.com
in Ghana wishing to determine the authenticity of the claim, selected sample of
residential properties to appraise their prices before and after the change of
government. The results, reported in GHc000, are:
Before After
128 135

105 110
119 131
140 142
98 105
123 130
127 131
115 110
122 125
145 149
At the 0.01 significance level:
a) Make your decision using the critical value approach.
b) What is the p-value? Decide with it
c) Mention one assumption that needs to be made about the
distribution of the differences?
d) Is the change of government associated with the higher prices
of residential homes? Justify practically.

Answer 1

a) we test the hypotheses;

H0: mean house before is equal to mean change after

H1: mean house before is less than after

Before After d d-$\bar d$ $(d-\bar d)^2$

128 135 -7 -2.4 5.76

105 110 -5 -0.4 0.16

119 131 -12 -7.4 54.76

140 142 -2 2.6 6.76

98 105 -7 -2.4 5.76

123 130 -7 -2.4 5.76

127 131 -4 0.6 0.36

115 110 5 9.6 92.16

122 125 -3 1.6 2.56

145 149 -4 0.6 0.36

Total -46 174.4

t=$\frac{\bar d}{\frac {sd}{\sqrt n}}$

=$\frac{\frac{-46}{10}}{\frac{{\sqrt\frac{174.4}{10-1}}}{\sqrt{10}}}$

t=-3.3045

The t value from the table is 2.8214

since the absolute value of the test statistic is greater than the table value, we reject the null hypothesis in favor of the alternative hypothesis.

b) From the t tables, the corresponding p-value to the test statistic is 0.004. since the p-value is less than 0.01, we reject the null hypothesis.

c) distribution of the differences is assumed to be normal.

d) Yes. this is because the mean of the differences gives a negative value implying the mean before change was lower than the mean after change . Rejection of the null hypothesis also implies that the change is statistically significant.