An executive believes that a new energy drink his company developed will increase an individual's stamina. In order to test this, he selects random individuals and times how long they can run without stopping. He then instructs the individuals to drink the energy drink for two weeks. After the two weeks, he times how long they can run again without stopping. Suppose that data were collected for a random sample of 35 people, where each difference is calculated by subtracting the time spent running before the two-week period from the time spent running after the two-week period. Assume that the times are normally distributed. The test statistic is t≈6.298, α=0.01, the corresponding rejection region is t>2.441, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd>0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero? Select all that apply: A) Fail to reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero. B) Reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero. C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero. D) Based on the results of the hypothesis test, there is enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.
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!
An executive believes that a new energy drink his company developed will increase an individual's stamina. In order to test this, he selects random individuals and times how long they can run without stopping. He then instructs the individuals to drink the energy drink for two weeks. After the two weeks, he times how long they can run again without stopping. Suppose that data were collected for a random sample of 35 people, where each difference is calculated by subtracting the time spent running before the two-week period from the time spent running after the two-week period. Assume that the times are
Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero?
Select all that apply:
A) Fail to reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero.
B) Reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero.
C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.
D) Based on the results of the hypothesis test, there is enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.
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