A random sample of 29 employees of a large company have their systolic blood pressure checked. Summary statistics are provided in the table below. Assume that the systolic blood pressure of all U.S. adults follows a normal distribution with a mean of 122 mm Hg and a standard deviation of 20 mm Hg. (a) Approximately what percent of all U.S. adults have a systolic blood pressure greater than 142 mm Hg? (b) Describe the distribution of systolic blood pressure for the 29 employees of this company that were sampled. (c) The company CEO wants to know if the mean systolic blood pressure of employees at her company is higher than the national average. State the hypotheses for testing this concern. (d) The conditions for the hypothesis test in part (c) were satisfied. The hypothesis test resulted in a t-score of 5.495 and a p-value of 3.591 × 10. Interpret the p-value in the context of this hypothesis test. What would this p-value lead you to conclude? (e) Explain in context what it would mean to make a type II error for the hypothesis test in parts (c) and (d). In addition to recording the systolic blood pressure of the 29 employees at the company, their ages were also recorded. A linear regression model was fit to these data. Graphical and numerical summaries of this analysis are given below. Use this information to answer the questions that follow. Predictor Coef SE Coef T P Constant 97.0771 5.5272 17.562 .000 Age 0.9493 .1161 8.174 .000 S=9.563 R-Sq=.712 (f) Interpret the slope of the regression line in this context. (g) Comment on the strength, direction, and form of the relationship between age and systolic blood pressur
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 random sample of 29 employees of a large company have their systolic blood pressure checked. Summary statistics are provided in the table below. Assume that the systolic blood pressure of all U.S. adults follows a
(a) Approximately what percent of all U.S. adults have a systolic blood pressure greater than 142 mm Hg?
(b) Describe the distribution of systolic blood pressure for the 29 employees of this company that were sampled.
(c) The company CEO wants to know if the mean systolic blood pressure of employees at her company is higher than the national average. State the hypotheses for testing this concern.
(d) The conditions for the hypothesis test in part (c) were satisfied. The hypothesis test resulted in a t-score of 5.495 and a p-value of 3.591 × 10. Interpret the p-value in the context of this hypothesis test. What would this p-value lead you to conclude?
(e) Explain in context what it would mean to make a type II error for the hypothesis test in parts (c) and (d).
In addition to recording the systolic blood pressure of the 29 employees at the company, their ages were also recorded. A linear regression model was fit to these data. Graphical and numerical summaries of this analysis are given below. Use this information to answer the questions that follow.
Predictor Coef SE Coef T P Constant 97.0771 5.5272 17.562 .000 Age 0.9493 .1161
8.174
.000
S=9.563
R-Sq=.712
(f) Interpret the slope of the regression line in this context.
(g) Comment on the strength, direction, and form of the relationship between age and systolic blood pressure.
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