A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r }
\text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \
\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \
\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \
\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \
\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \
\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \
\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \
\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \
\hline & & & & \
\hline 22.40 & \text { chi-square } & & & \
\hline .0001 & \text { p-value } & & &
\end{array}$$
At a significance level of .05,what is the appropriate rejection point condition?

Question

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r } 
\text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \
\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \
\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \
\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \
\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \
\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \
\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \
\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \
\hline & & & & \
\hline 22.40 & \text { chi-square } & & & \
\hline .0001 & \text { p-value } & & &
\end{array}$$
At a significance level of .05,what is the appropriate rejection point condition?

Quizplus · Accepted Answer

The appropriate rejection point condition for a chi-square goodness of fit test with 5 degrees of freedom and a significance level of .05 is to reject H₀ if χ² > 11.0705. This value can be found in the chi-square distribution table or using a calculator with a chi-square distribution function. Since the calculated chi-square value from the data (22.40) is greater than the rejection point (11.0705), the null hypothesis, that the data follows a normal distribution, is rejected.

A Real Estate Company Is Analyzing the Selling Prices of Residential