Concept explainers
a)
To identify the population and parameter.
a)
Answer to Problem 40E
The population is all students who attend the school and parameter is proportion of students who the student body president knows the name of.
Explanation of Solution
Given:
First need to understand about population and parameter.
Population: It is the set of all the possible individuals possessing the characteristic of interest in a study.
Parameter: A parameter is a numerical characteristic based on observations from the entire population of objects in a study.
In this study, population is all students who attend the school and parameter is proportion of students who the student body president knows the name of.
b)
To explain whether the conditions for calculating a confidence interval for the population proportion.
b)
Answer to Problem 40E
All the conditions are met.
Explanation of Solution
Given:
The condition of random selection is satisfied because the sample is SRS.
The sample should be less than 10% of the population. Here, 100 students’ chips are less than 10% of all the 1800 students in population. Hence, this condition met.
The last condition is, number of success and failure must be
c)
To construct 99% confidence interval for a proportion.
c)
Answer to Problem 40E
The 99% confidence interval for a proportion is 0.3317 < p < 0.5883
Explanation of Solution
Given:
Confidence level = 0.99
Formula:
Sample proportion:
Margin of error:
The confidence interval:
The confidence level = 0.99
So, level of significance = a=0.01
The zc=z a/2 critical value = 2.575 …Using excel formula, =ABS(NORMSINV(0.01/2))
The sample proportion is,
The margin of error is,
The confidence interval is,
Hence, the 99% confidence interval for population proportion is 0.3317 < p < 0.5883
d)
To interpret confidence interval.
d)
Answer to Problem 40E
We are 99% confident that the true population proportion is between 0.3317 and 0.5883
Explanation of Solution
Given:
The 99% confidence interval for population proportion is 0.3317 < p < 0.5883
We are 99% confident that the true population proportion of all students that the students body president knows is 0.3317 and 0.5883
Chapter 8 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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