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An experiment was conducted by students at The Ohio State University in the fall of 1993 to explore the nature of the relationship between a person's heart rate and stepping up anddown on steps of various heights. One of the objectives of this study was to see whether thehight of steps matters. Students were randomly assigned to two groups: Low-steps, wherethe height of steps was 5.75 inches (this group was coded as 0), and High-steps, where theheight of steps was 11.5 inches (this group was coded as 1). Student performed the exercise(stepping up and down) for three minutes, after which their heart rates were measured. Theinvestigators had hypothesized that the average heart rate would be di erent between thetwo groups. A two-sample t-test was used to analyze the data. The results are shown below.Answer the following questions:
a- Explain why we use a two-sample t-test and not a z-test or a paired t-test.
b- Is this a one-sided or two-sided test?
c- Is the relationship between heart rate and the height of steps statistically signi cant at0.01 level? Write down the t-score and p-value.
d- Alternatively, the investigators could do the experiment as follows: ask each student to dothe exercise with a low-step rst, measure his/her heart rate, ask him/her to relax for awhile, then repeat the exercise with a high-step, and measure his/her heart rate again.What type of hypothesis testing method you would recommend in this case? Why?
As part of the National Health and Nutrition Examination Survey, the Department of Health and Human Services obtained self-reported heights and measured heights for males aged 12-16. All measurement is in inches. Listed below are sample results.
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Find the 90%, 95% and 99% confidence intervals for the proportion of all voters who favor the issue. How many more voters should we include in the sample if we need to reduce the margin of error by half?
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