## Related questions with answers

Does increasing the amount of calcium in our diet reduce blood pressure? Researchers designed a randomized comparative experiment to find out. The subjects were 21 healthy black men who volunteered to take part in the experiment. They were randomly assigned to two groups: 10 of the men received a calcium supplement for 12 weeks, while the control group of 11 men received a placebo pill that looked identical. The experiment was double-blind. The response variable is the decrease in systolic (top number) blood pressure for a subject after 12 weeks, in millimeters of mercury. An increase appears as a negative number. Here are the data.

$\begin{array}{|l|r|r|r|r|r|r|r|r|r|r|r|} \hline \begin{array}{l} \text { Group 1 } \\ \text { (calcium) } \end{array} & 7 & -4 & 18 & 17 & -3 & -5 & 1 & 10 & 11 & -2 & \\ \hline \begin{array}{l} \text { Group 2 } \\ \text { (placebo) } \end{array} & -1 & 12 & -1 & -3 & 3 & -5 & 5 & 2 & -11 & -1 & -3 \\ \hline \end{array}$

Researchers want to know if a calcium supplement reduces blood pressure more than a placebo, on average, for healthy black men like these. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

Solution

VerifiedGiven claim: Mean is lower for calcium (reduces)

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of the null hypothesis.

$\begin{align*} H_0&:\mu_1= \mu_2 \\ H_a&: \mu_1 <\mu_2 \end{align*}$

where

$\mu_1$=true mean blood pressure of healthy men that receive a calcium supplement

$\mu_2$=true mean blood pressure of healthy men that receive a placebo

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