Statistical Inference A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 2.1 moles per liter, the reaction was run 18 times, with an average velocity of 15 micro-moles per 60 minutes and a standard deviation of 1.5. With a substrate concentration of 2.7 moles per liter, 14 runs were made, yielding an average velocity of 18 micromoles per 60 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.6 micromole per 60 minutes (?2 − ?1 > 0.6)? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances.
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!
Statistical Inference
A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 2.1 moles per liter, the reaction was run 18 times, with an average velocity of 15 micro-moles per 60 minutes and a standard deviation of 1.5. With a substrate concentration of 2.7 moles per liter, 14 runs were made, yielding an average velocity of 18 micromoles per 60 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.6 micromole per 60 minutes (?2 − ?1 > 0.6)? Use a 0.01 level of significance and assume the populations to be approximately
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