- Complete a one-sample [latex]t[/latex]-test for means from hypotheses to conclusions.
In this section, we will learn to conduct a hypothesis test about a population mean and state a conclusion in context under appropriate conditions.
We did hypothesis tests previously. The steps and logic in conducting a hypothesis test about a population mean are the same as the a hypothesis test involving population proportions.
- Write out the null and alternative hypotheses.
- Check the conditions for the hypothesis test.
- Calculate a test statistic.
- Calculate a P-value.
- Compare the P-value to the significance level, [latex]\alpha[/latex], to make a decision.
Decision Conclusion If P-value [latex]\le\alpha[/latex], there is enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data provide convincing evidence in support of the alternative hypothesis. If P-value [latex]\gt\alpha[/latex], there is not enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis. - Write a conclusion in context (e.g., we do/do not have convincing evidence…).
Plastics Pollution
Plastic pollution has become one of the most pressing environmental issues, as rapidly increasing production of disposable plastic products overwhelms the world’s ability to deal with them.[1] The United States welcomes the historic opportunity at the United Nations Environment Assembly (UNEA 5.2), February-March 2022, to start a process with other nations and stakeholders to fight plastic pollution. The United States is already acting both domestically and internationally to address this global challenge.[2]
What about us? Are you aware of how much plastic we are using in our lives?
Before we get into the details, let’s practice identifying research questions, writing the hypotheses accordingly, and knowing the steps in conducting a hypothesis test that involves a population mean.
- Notation for population mean: [latex]\mu[/latex] (pronounce as “mu”)
- Notation for sample mean: [latex]\bar{x}[/latex] (pronounce as “x-bar”)