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Dr. Alvarez, a nutrition researcher, believes there is an association between a patient’s daily sugar intake, X (in grams), and their fasting blood‑glucose level, Y (in mg/dL). He tests his family and friends and the following paired data points are collected.
Write down the sampling method used by Dr. Alvarez.
State one drawback of this sampling method.
State suitable hypotheses H0 and H1 for a two-tailed test of Dr. Alvarez's claim.
Carry out the test at the 5% significance level. With reference to the p-value, state your conclusion in the context of Dr. Alvarez's claim.
Dr. Alvarez fits the regression line of Y on X as Y^=0.50X+80.0.
She uses this to predict that her brother, who consumes 150g of sugar will have a fasting glucose of 155mg/dL.
Comment on the validity of this prediction with a mathematical justificiation.
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