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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Answer A1, A2 and B1:
A. Refer to the data about the height 100 senior high school student. Assume this as your target population. Suppose this data constitute a
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- 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.
B. A study is conducted to test the hypothesis that people with glaucoma have higher-than-average blood pressure. The study includes 200 people with glaucoma whose mean Systolic Blood Pressure (SBP) is 140 mm Hg with a standard deviation of 25 mm Hg.
1. Construct a 95% CI for the true mean SBP among people with glaucoma.
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