rbohydrate consumption to less than 20 grams per day for one year. They measured the men’s systolic blood pressure at the beginning and at the end of the study. The average reduction in systolic blood pressure for the 30 men was 5.5 point
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!
Medical researchers took a random sample of 30 men from a list of 1274 volunteers. They put the men on a diet that restricted carbohydrate consumption to less than 20 grams per day for one year. They measured the men’s systolic blood pressure at the beginning and at the end of the study. The average reduction in systolic blood pressure for the 30 men was 5.5 points. Assume that the population standard deviation is 1.8 points, and that the researchers hope to estimate the true
- State the research question.
- State the parameter of interest.
- Check the conditions needed for writing a valid confidence interval. There are three conditions. State each condition and whether it is met in this study.
- Calculate a 90% confidence interval for the population mean.
- Interpret the confidence interval in context.
Note:
As per the guidelines, we are only allowed to solve three subparts, please post the other questions as a different question.
1.
- The research question is to find the true mean reduction in systolic blood pressure for men.
2.
The parameter is defined as the numerical descriptive measure of the population.
- For this case, the true mean reduction in systolic blood pressure for all men can be considered as the population parameter because it represents the characteristic of all the mn (population).
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