Introduction to Probability and Statistics
Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 9, Problem 9.52SE

i.

To determine

To explain:

  α and β for a statistical hypothesis test.

i.

Expert Solution
Check Mark

Answer to Problem 9.52SE

The significance level and the probability of making a Type II error is denoted by letterαand βrespectively.

Explanation of Solution

The significance level of the hypothesis is denoted by the letter α . It is the rejection probability when the null hypothesis is true.

For example,

The difference exists when there is no actual difference is denoted by 5% risk or a significance level of 0.05 .

The beta level (often simply called beta) is the probability of making a Type II error (accepting the null hypothesis when the null hypothesis is false).

Conclusion:

The significance level and the probability of making a Type II error is denoted by letter α and β respectively.

ii.

To determine

To explain:

The change in the value of β if the value of α is decreases.

ii.

Expert Solution
Check Mark

Answer to Problem 9.52SE

On decreasing the value of αthe value of βwill increases.

Explanation of Solution

The significance level of the hypothesis is denoted by the letter α . It is the rejection probability when the null hypothesis is true.

The beta level (often simply called beta) is the probability of making a Type II error (accepting the null hypothesis when the null hypothesis is false).

For a fixed sample size, if value of α decreases then value of β will increases.

Conclusion:

Therefore, if value of α decreases then value of β will increases

iii.

To determine

To explain:

The change in sample on decreasing α and β .

iii.

Expert Solution
Check Mark

Answer to Problem 9.52SE

On decreasing the values of α and β , the sample size is increases.

Explanation of Solution

The significance level of the hypothesis is denoted by the letter α . It is the rejection probability when the null hypothesis is true.

The beta level (often simply called beta) is the probability of making a type II error (accepting the null hypothesis when the null hypothesis is false).

The sample size is increases on decreasing the values of α and β

Conclusion:

Therefore, the sample size is increases on decreasing the values of α and β .

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Chapter 9 Solutions

Introduction to Probability and Statistics

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