Answer Happy

Almost 100 million Christmas trees are sold each year in Europe and North America. Certain forest administration makes the selection of trees that would be cut anyway (for health of the forest, e.g. trees that are densely plant ed etc.) for Christmas sale only shortly before Christmas. Such trees need not be considered very beautiful, however, the demand for them is very high every year. To decide about the price, foresters divide the cut trees, for simplicity, into three price groups with similar tree height within each group. You, as a customer, are interested in buying a tree from the middle group where the trees are supposed to be approximately 150 cm tall. In order to verify this information, the forester measured the height in a sample of twenty trees from this group. The measured heights in cm are displayed in Table 1. 132 135 156 158 141 143 143 162 163 166 145 147 149 166 167 169 151 174 155 176 Table 1: Observations for Problem 25, heights of trees in meters You can assume normality of the trees' height. i) What is the 98% confidence interval for mean height of the trees in this group? ii) If, additionally, we assume that the standard deviation is known and equal to 15 cm, how does the confidence interval from part i) change?