The data in the table below are summary statistics of the daily output (in tonnes) of random, independent samples of 6 copper mines in Free State, 8 copper mines in Northern Cape and 6 copper mines in Mpumalanga. Assume that the daily output of copper mines is normally distributed in all three countries. Daily copper mine output Free state Northern Cape Mpumalanga Sample mean 501 739 779 Sample standard deviation 169 195 221 a. Perform a one-way analysis of variance (ANOVA) to determine the following: SSTr, SSE, SST, MSTr, MSE and F statistic. b. At the 5% level, test the hypothesis that the mean daily output levels of copper mines in these three provinces are equal. (In answering this question, clearly state the null and alternative hypotheses, test statistic and critical value). c. Use Fisher's least significant difference (LSD) procedure to determine whether: (1) the means of 6 Free State copper mines and 8 copper mines in Northern Cape differ from each other and (2) the means of 8 copper mines in Northern Cape and 6 copper mines in Mpumalanga differ from each other. Perform these pairwise comparison tests at the 5% level.
The data in the table below are summary statistics of the daily output (in tonnes) of random, independent samples of 6 copper mines in Free State, 8 copper mines in Northern Cape and 6 copper mines in Mpumalanga. Assume that the daily output of copper mines is
Daily copper mine output | Free state | Northern Cape | Mpumalanga |
Sample |
501 | 739 | 779 |
Sample standard deviation | 169 | 195 | 221 |
a. Perform a one-way analysis of variance (ANOVA) to determine the following: SSTr, SSE, SST, MSTr, MSE and F statistic.
b. At the 5% level, test the hypothesis that the mean daily output levels of copper mines in these three provinces are equal. (In answering this question, clearly state the null and alternative hypotheses, test statistic and critical value).
c. Use Fisher's least significant difference (LSD) procedure to determine whether: (1) the means of 6 Free State copper mines and 8 copper mines in Northern Cape differ from each other and (2) the means of 8 copper mines in Northern Cape and 6 copper mines in Mpumalanga differ from each other. Perform these pairwise comparison tests at the 5% level.
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