A special diet is intended to reduce systolic blood pressure. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 35 patients with high blood pressure had an average systolic blood pressure of , with standard deviation s = 23. Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of systolic blood pressure for patients in this group is approximately Normal. sample mean is 143 In order to test if the diet reduces systolic blood pressure to the desired target, state the null hypothesis and alternative hypothesis. Calculate the t value for the test? (round to 3 decimal places) How many degrees of freedom for this test? If we decide to test at a level of significance of is there evidence to support the claim that the diet reduces systolic blood pressure to the desired target? What is the 95% confidence interval for the average systolic blood pressure of patients in this group? (round to 2 decimal places after all calculations)
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 special diet is intended to reduce systolic blood pressure. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 35 patients with high blood pressure had an average systolic blood pressure of , with standard deviation s = 23. Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of systolic blood pressure for patients in this group is approximately Normal.
sample
In order to test if the diet reduces systolic blood pressure to the desired target, state the null hypothesis and alternative hypothesis.
Calculate the t value for the test? (round to 3 decimal places)
How many degrees of freedom for this test? If we decide to test at a level of significance of is there evidence to support the claim that the diet reduces systolic blood pressure to the desired target?
What is the 95% confidence interval for the average systolic blood pressure of patients in this group? (round to 2 decimal places after all calculations)
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