A coach uses a new technique to train gymnasts. Seven gymnasts were randomly selected and their competition scores were recorded before and after the training. The results, assumed to be Normal, are shown below: Before: Average=9.571, standard deviation=0.076 After: Average=9.629, standard deviation=0.180 Before - After: Average= -0.058, standard deviation=0.172 Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts' scores. Round your answer to 3 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!
A coach uses a new technique to train gymnasts. Seven gymnasts were randomly selected and their competition scores were recorded before and after the training. The results, assumed to be Normal, are shown below:
Before: Average=9.571, standard deviation=0.076
After: Average=9.629, standard deviation=0.180
Before - After: Average= -0.058, standard deviation=0.172
Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts' scores. Round your answer to 3 decimal places.
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