Statistics Question

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A study of human body temperature as affected by ambient air temperature and a dietary supplement that is hoped to increase heat tolerance. Body temperatures (°C) were measured for 125 athletes immediately following a standard exercise routine in a room controlled to a fixed air temperature (°C). The air temperatures were fixed at 21°C, 25°C, 29°C and 33°C. Each subject had either been receiving a placebo dose, a half dose or a full dose of the dietary supplement. Age and BMI was also measured for each subject. Table 1. Descriptive StatisticsCategorical Variablesn (%)Air Temperature (°C)    21 °C23 (18.4)   25 °C40 (32.0)   29 °C37 (29.6)   33 °C25 (20.0)Supplement Dose    Placebo41 (32.8)   Half41 (32.8)   Full43 (34.4) Continuous VariablesMean (SD)Body Temperature (°C)36.99 (0.15)Age (years)34.77 (3.74)BMI26.34 (2.73)Table 2. The ANOVA TableSourceType 1 SSAge0.0246BMI0.0000Dose0.1158Air Temp0.1596Air Temp×Dose0.2616Error2.1845

Test for a Dose effect on Body Temperature adjusting for Age and BMI. Interpret your findings.

1. Test for an Air Temperature effect on Body Temperature adjusting for Age, BMI and Dose. Interpret your findings.

Does the effect of Air Temperature on Body Temperature depend on the supplement dose? Perform a test and interpret your findings.

The same 125 subjects from problem 1 are used for this problem. Using the information below, answer the following questions.Table 3. The Parameter Estimates from a
Multiple Linear RegressionParameterEstimateIntercept37.125Age-0.001BMI-0.002ATemp33-0.023ATemp29-0.157ATemp25-0.093Full Dose0.039Half Dose-0.042Temp33*Full-0.192Temp33*Half-0.058Temp29*Full0.107Temp29*Half0.056Temp25*Full0.073Temp25*Half0.029Table 4. The Adjusted Mean Body Temperature for each fixed Air Temperature at a Full Dose of the Dietary SupplementAir TempMean Body Temp (°C)21 °C37.0825 °C37.0629 °C37.0333 °C36.86

Write down the model in Table 3.

Use the adjusted means in Table 4 to perform multiple comparisons using the Bonferroni Method at an overall significance level of 0.05. Test the following hypotheses:

i. Ho : /21 = 125  

ii. Ho : M25 = M29 

Ho : /29 = M33

After performing these comparisons, what do you conclude?