(a)
To explain the null hypothesis and the alternative hypothesis and write their symbols
(a)
Explanation of Solution
Given information:
A company manufactures classroom chairs for the high school students. The mean breaking strength of the chairs is
Let
The null hypothesis is the hypothesis that is considered to be true.
It is denoted as
Define the null hypothesis
One of the chairs with weight less than
Define the alternate hypothesis
(b)
To explain: What is Type I and Type II error and what are the consequences of each.
(b)
Explanation of Solution
Type I error is defined as the error when
The null hypothesis
The mean breaking strength of the chair is
Type II error is defined as the error when
The alternate hypothesis is
This indicates that the mean breaking strength of the chair is less than
In the given problem, Type II error indicate that the chances of collapsing a chair are less.
Type II error indicate that the chance that chair will collapse are more.
(c)
To find out: Out of the significance levels given below which is recommended.
- 0.01
- 0.05
- 0.10
(c)
Explanation of Solution
Given Information : The three level of significance
Type I error is defined as the error when
The null hypothesis
Type II error is defined as the error when
The alternate hypothesis is
In response to the given problem, Type I error indicate that chair will collapse less.
Type II error indicate that the chair will collapse more often.
The main objective is to keep the Type II error as less as possible as its more serious.
This will happen when Type I error
The value
Out of the given values
The greatest value is
Therefore, choose significance level
(d)
To explain: the meaning of Power of Test.
(d)
Explanation of Solution
Given Information: The power of the test to detect
The null hypothesis
The alternate hypothesis is
The power of the test to detect
The power of the test is defined as the probability of rejecting the null hypothesis if the alternative hypothesis is true.
The power of the test is
(e)
To find out: the ways the increase the power of the test
(e)
Explanation of Solution
The following are the ways the increase the power of the test.
- Increase the
sample size : Increasing the sample size will give better estimation. - Increase the level of significance: This will increase the probability of committing a Type I error which will decrease the Type II error. Therefore, by definition it will increase the power of test.
Chapter 9 Solutions
The Practice of Statistics for AP - 4th Edition
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