Question

A college has decided to introduce the use of plus and minus with letter grades, as long as there is convincing evidence that more than $60 \%$ of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If $p$ represents the proportion of all faculty who favor a change to plus-minus grading, which of the following pairs of hypotheses should be tested? $$ H_{0^{*}} p=0.6 \text { versus } H_{i}: p<0.6 $$ or $$ H_{0}: p=0.6 \text { versus } H_{e}: p>0.6 $$ Explain your choice.

Name: Problem 15, Chapter 10: Statistics Learning From Data
Uploaded: 2021-02-03T15:57:10-08:00
Duration: 1 min 30 s
Channel: Hossam Mohamed

   A college has decided to introduce the use of plus and minus with letter grades, as long as there is convincing evidence that more than $60 \%$ of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If $p$ represents the proportion of all faculty who favor a change to plus-minus grading, which of the following pairs of hypotheses should be tested?
$$
H_{0^{*}} p=0.6 \text { versus } H_{i}: p<0.6
$$
or
$$
H_{0}: p=0.6 \text { versus } H_{e}: p>0.6
$$
Explain your choice.

Statistics Learning From Data

Thomas H. Short,… 2nd Edition

Chapter 10, Problem 15

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Solved by Expert Hossam Mohamed

02/03/2021

Step 1

The college wants to introduce a new grading system (plus and minus with letter grades) but will only do so if there is convincing evidence that more than 60% of the faculty support the change. This sets up a scenario where we need to test the proportion of Show more…

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A college has decided to introduce the use of plus and minus with letter grades, as long as there is convincing evidence that more than $60 \%$ of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If $p$ represents the proportion of all faculty who favor a change to plus-minus grading, which of the following pairs of hypotheses should be tested? $$ H_{0^{*}} p=0.6 \text { versus } H_{i}: p<0.6 $$ or $$ H_{0}: p=0.6 \text { versus } H_{e}: p>0.6 $$ Explain your choice.

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Key Concepts

Null Hypothesis

The null hypothesis (H0) represents the default assumption about the parameter—in this case, that the proportion equals a specified benchmark (p = 0.6). It is assumed to be true unless there is sufficient statistical evidence to reject it.

Alternative Hypothesis

The alternative hypothesis (Ha) embodies the claim the researcher wants to gather evidence for. Here, since the decision depends on whether more than 60% of the faculty support the change, the appropriate alternative hypothesis is p > 0.6.

One-tailed Test

A one-tailed test is used when the research question is directional, meaning that the interest is only in determining if the parameter is greater (or less) than a specific value. In this context, testing p > 0.6 focuses solely on whether the proportion exceeds the benchmark.

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