Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σx = 63.8; Σx2 = 520.96; Σy = 89.8; Σy2 = 1046.96; Σxy = 731.35 x 6.2 8.7 7.0 7.5 8.1 6.9 10.0 9.4 y 9.7 10.8 10.5 11.3 14.2 7.0 14.1 12.2 (c) Find the sample correlation coefficient r and the sample coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = (d) If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml (e) Use level of significance 1% and test the claim that the population correlation coefficient ρ is not zero. (Round your test statistic to three decimal places.)
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!
Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information.
| x | 6.2 | 8.7 | 7.0 | 7.5 | 8.1 | 6.9 | 10.0 | 9.4 |
| y | 9.7 | 10.8 | 10.5 | 11.3 | 14.2 | 7.0 | 14.1 | 12.2 |
| r = | |
| r2 = |
Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.)
| lower limit | mg/10 ml |
| upper limit | mg/10 ml |
(e) Use level of significance 1% and test the claim that the population correlation coefficient ρ is not zero. (Round your test statistic to three decimal places.)
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