The table below contains summary statistics about the trading density (sales per square metre, R/m2) for two random and independent samples of 18 housing developments in the Western Cape, and 13 housing developments in the Free State. Assume that the trading densities of the Western Cape and the Free State housing developments are normally distributed. Housing cost Western cape Free state Sample mean (R) 2500.2 2100.7 Sample standard deviation (R) 820.3 694.6 a. Estimate a 95% confidence interval for the standard deviation of the cost of housing developments in the Free State. b. Are the variances of the trading densities of housing developments in the Western Cape and the Free State are the same? Test at the 10% level. (Note: In answering this question, make sure you state the following: null and alternative hypotheses, test statistic and critical value. Write your final answers to 3 decimal places). c. Estimate a 90% confidence interval for the difference between the mean trading densities of housing developments in the Western Cape and the Free State are the same. Use the conclusion of the test conducted in (b) to inform your choice about the standard error that should be used to estimate this 90% confidence interval
The table below contains summary statistics about the trading density (sales per square metre, R/m2) for two random and independent samples of 18 housing developments in the Western Cape, and 13 housing developments in the Free State. Assume that the trading densities of the Western Cape and the Free State housing developments are normally distributed.
| Housing cost | Western cape | Free state |
| Sample mean (R) | 2500.2 | 2100.7 |
| Sample standard deviation (R) | 820.3 | 694.6 |
a. Estimate a 95% confidence interval for the standard deviation of the cost of housing developments in the Free State.
b. Are the variances of the trading densities of housing developments in the Western Cape and the Free State are the same? Test at the 10% level. (Note: In answering this question, make sure you state the following: null and alternative hypotheses, test statistic and critical value. Write your final answers to 3 decimal places).
c. Estimate a 90% confidence interval for the difference between the mean trading densities of housing developments in the Western Cape and the Free State are the same. Use the conclusion of the test conducted in (b) to inform your choice about the standard error that should be used to estimate this 90% confidence interval.
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