A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rate in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations are normally distributed. The test statistic is t≈5.627, α=0.05, the corresponding rejection regions are t<−2.228 and t>2.228, 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 heart rate in the 75∘F room and the heart rate in the 50∘F room is significantly not equal to zero? Select all that apply: A) Reject the null hypothesis that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is equal to zero. B) Fail to reject the null hypothesis that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is equal to zero. C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is not equal to zero. D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is not equal to 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!
A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rate in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations 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 heart rate in the 75∘F room and the heart rate in the 50∘F room is significantly not equal to zero?
Select all that apply:
A) Reject the null hypothesis that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is equal to zero.
B) Fail to reject the null hypothesis that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is equal to zero.
C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is not equal to zero.
D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the heart rate in the 75∘F room and the heart rate in the 50∘F room is not equal to zero.
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