The Realtor for an Exclusive,planned Housing Development Says That House $\sigma ^ { 2 } > 64$

Essay

The realtor for an exclusive,planned housing development says that house prices average $125 thousand and uniformity of prices within the development is indicated by the standard deviation of $ $\sigma ^ { 2 } > 64$ 8 thousand.A prospective buyer wants to check on the uniformity of prices and randomly samples 12 houses and determines the selling price.These data are: 113.0,126.2,134.4,129.4,106.6,117.4,123.5,121.0,109.6,119.4,126.6,and 119.6.Use these data to test the hypothesis:
H₀: $\sigma ^ { 2 } \leq 64$ (realtor correct)
H₁: (realtor incorrect)
The buyer assumes selling prices are normally distributed and employs a 0.05 significance level.Is the statement by the realtor correct?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: _____________________
Interpretation: _____________________________________