Refer to the data about the height 100 senior high school student. Assume this as your target population. Suppose this data constitute a normal distribution. 156 182 154 146 160 156 160 139 162 137 158 145 155 157 150 152 165 149 150 171 162 144 141 156 148 165 157 167 154 169 167 162 166 163 154 129 166 153 164 156 152 160 160 155 162 167 147 160 168 142 135 145 146 150 169 156 186 155 158 156 144 160 148 175 153 157 152 150 158 157 151 165 163 159 173 145 162 157 150 152 144 138 168 158 159 141 161 160 151 163 161 168 164 165 164 139 161 136 173 163   Suppose we had generated 1000 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean? When we construct a 90% confidence interval, we say that “we are 90% confident that the true population mean lies within the confidence interval”. Explain what we mean by this phrase.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...