1. a) What are the two decisions that you can make from performing ahypothesis test?b) In your own words, after learning about hypothesis tests, how isthat decision made?c) Discuss the types of errors that can be made when performing a hy-pothesis test.d) Why can't we just survey all the population to find u and not haveto do a hypothesis test?

Answered: 1. a) What are the two decisions that…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 4SE: What is the difference between events and outcomes? Give an example of both using the sample space...

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1. a) What are the two decisions that you can make from performing a
hypothesis test?
b) In your own words, after learning about hypothesis tests, how is
that decision made?
c) Discuss the types of errors that can be made when performing a hy-
pothesis test.
d) Why can't we just survey all the population to find u and not have
to do a hypothesis test?

Expert Solution

Step 1

(a) Two decisions that can be made based on the result of a hypothesis test are:

Reject the null hypothesis
Fail to reject the null hypothesis.

(b) Decision is made based on the significance level and p-value:

Significance level refers to the degree of significance in which we accept or reject the null hypothesis. We usually take $α = 0.05$ , indicating that there is 5% chance of rejecting the null hypothesis, when it is true.

P-value is the probability of obtaining the value of the test statistic or a value more extreme, assuming the null hypothesis is true.

We reject $H_{0}$ : If the p-value is less than the significance level.

Fail to reject $H_{0}$ : If the p-value is greater than the significance level.

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