Inferential Statistics
(c) Carry out a test of significance to decide whether Cal Poly students tend to carry less than 10% of their body weight.
1. Define the parameter(s) of interest. [Hint: Is the response variable quantitative or categorical?]
2. State the hypotheses both in symbols and in words.
3. Identify an appropriate test procedure and state and if a theory-based test comment on the validity conditions.
4. Use technology to determine a test statistic and p-value for these hypotheses.Also report a 95% confidence for the parameter of interest.
Press one of the links below to view the appropriate technology instructions.
- From your previous results, use the ratio hot spot to select Test Mean
- Specify the hypothesized value of the population mean.
- Press OK
- For the confidence interval: Retrace your steps and select Confidence Interval > 0.95.
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- Choose Stat > Basic Statistics > One Sample t
- Double click on the ratio variable so it appears in the One or more samples box.
- Check the box to Perform hypothesis test and specify the hypothesized value of the population mean.
- Press the Options button and choose the form of the alternative hypothesis.
- Press OK
- For the confidence interval: Retrace your steps and use a two-sided alternative.
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- t.test(backpackdata$ratio, mu=XX, alternative="XXX")
- Enter the hypothesis population mean for XX.
- Enter less, greater, or two.sided for XXX.
- For the confidence interval: Retrace your steps use "two.sided" for the alternative.
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- Open the Theory Based Inference applet.
- Use the pull-down menu to select the One mean scenario.
- Check the Paste data and Includes header boxes.
- Paste in the ratio data from the Excel file.
- Press Use Data. (You should be able to verify the sample size, mean, and standard deviation values.
- Check the Test of significance box. Specify the hypothesized value for the population mean and toggle the alternative direction. Press Calculate
- For the confidence interval: check the Confidence interval box.
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Copy the relevant output into your report.
5. State your decision and summarize your conclusions in context. Be sure to reference information from the output! (Meaning, cite the test statistic, p-value, and confidence interval!)
