Inferential Statistics
(g) Carry out a test of significance to decide whether Cal Poly students with back problems tend to carry more weight (higher ratios) than those without back problems.
1. Define the parameter(s) of interest.
2. State the hypotheses both in symbols and in words.
3. Identify an appropriate test procedure and state and if a theory-based approach comment on the validity conditions.
4. Use technology to find the test statistic and p-value for this procedure and these hypotheses. Include a 95% confidence interval 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 t Test
- Which is the appropriate p-value? Where is the confidence interval?
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- Choose Stat > Basic Statistics > Two Sample t
- Specify the ratio variable in the Samples box and the Backproblems variable in the Sample IDs box.
- Under Options change the direction of the Alternative hypothesis.
- Press OK twice.
- Note: If using a one-sided alternative, you will need to retrace your steps and use a two-sided alternative to find a 95% confidence interval.
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- t.test(backpackdata$ratio~backpackdata$Backproblems, alternative="XXX")
- Enter less, greater, or two.sided for XXX. Note: You may have to run the command once to see in which direction R is subtracting.
- For the confidence interval: Retrace your steps use "two.sided" for the alternative.
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- Continuing with the Theory Based Inference applet, check the Test of significance box and specify the direction of the alternative. 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 computer output!
