Concept explainers
(a)
To find: the type of design was used to gather this information.
(a)
Answer to Problem 18E
Prospective observational study
Explanation of Solution
This is a prospective study of observation. A prospective study defines and looks at a group of individuals (here, people with heart disease) in the future.
(b)
To Write: the suitable hypotheses.
(b)
Answer to Problem 18E
Explanation of Solution
Here want to evaluate how depressed patients are more likely to die than non-depressed patients among people who suffer from heart disease. Let
(c)
To explain: to satisfy the assumptions and conditions required for conclusion.
(c)
Explanation of Solution
it is assuming that samples have been randomly chosen. The overall sample size is less than 10 percent of all heart disease sufferers. Since the samples were randomly chosen, it is fair to assume that the two groups are independent. The number of successes is 67 among the 361 patients without depression, and the number of failures is 361-67 = 294, and the number of successes is 26 among the 89 patients with mild or severe depression, and the number of failures is 89-26 = 63. These numbers, for each group, are at least 10.
The assumptions and conditions required to satisfy the inference.
(d)
To Test: the hypothesis and state the conclusion.
(d)
Explanation of Solution
Given:
Formula used:
Calculation:
Pool the sample data.
Estimating
The observed difference
The z-score is
The P-value is
P-value=0.0131 is very small; the null hypothesis should not be accepted. It might infer that depressed patients are more likely to death than nondepressed ones among people who suffer from heart disease.
(e)
To Explain: the means of P-value.
(e)
Explanation of Solution
The P-value is the likelihood that a test statistic would be as large as or greater than the observed value if the null hypothesis is valid. So, if the P-value is 0.0131, this means that there is only a 1.31 percent probability that normal variance in sampling will generate a 10.65 percent difference in the sample proportion when this difference is actually 0.0.
(f)
To find: the type of error committed if the statement is actually incorrect.
(f)
Answer to Problem 18E
Type I
Explanation of Solution
It is rejected the null hypothesis here. If, indeed, the inference is false. This implies that, although it is valid, the null hypothesis is denied. So, it made an error with Type I.
Chapter 22 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Statistics for Psychology
Elementary Statistics (13th Edition)
Elementary Statistics: Picturing the World (6th Edition)
Elementary Statistics Using Excel (6th Edition)
Statistics for Business and Economics (13th Edition)
Basic Business Statistics, Student Value Edition
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