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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l }
\text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \
10 & 3.192 & 6.808 & 14.520 & 64.81 \
23 & 19.026 & 3.974 & 0.830 & 3.70 \
37 & 47.782 & -10.782 & 2.433 & 10.86 \
40 & 47.782 & -7.782 & 1.267 & 5.66\
27 & 19.026 & 7.974 & 3.342 & 14.92 \
3 & 3.192 & -0.192 & 0.012 & 0.05 \
140 & 140.000 & 0.000 & 22.404 & 100.00\22.40 & \text { Chi-square } \
.0001 & \text { p-value }
\end{array}$$
-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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } 
\text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \
10 & 3.192 & 6.808 & 14.520 & 64.81 \
23 & 19.026 & 3.974 & 0.830 & 3.70 \
37 & 47.782 & -10.782 & 2.433 & 10.86 \
40 & 47.782 & -7.782 & 1.267 & 5.66\
27 & 19.026 & 7.974 & 3.342 & 14.92 \
3 & 3.192 & -0.192 & 0.012 & 0.05 \
140 & 140.000 & 0.000 & 22.404 & 100.00\22.40 & \text { Chi-square } \
.0001 & \text { p-value }
\end{array}$$
-At a significance level of .05,what is the appropriate rejection point condition?

Quizplus · Accepted Answer

The chi-square goodness of fit test uses critical values from the chi-square distribution table. The degrees of freedom for this test are calculated as the number of classes minus 1 minus the number of parameters estimated from the data. Since there are 6 classes and no parameters mentioned as being estimated (assuming normal distribution parameters, mean and standard deviation, are estimated from the data), the degrees of freedom would be 6 - 1 - 2 = 3. At a significance level of .05 and 3 degrees of freedom, the critical value from the chi-square distribution table is 7.81473. Therefore, the rejection point condition is to reject the null hypothesis if the chi-square statistic is greater than 7.81473.

A Real Estate Company Is Analyzing the Selling Prices of Residential