Question

Calcium and Blood Pressure Does increasing the amount of calcium in our diet reduce blood pressure? Examination of a large sample of people revealed a relationship between calcium intake and blood pressure. The relationship was strongest for black men. Such observational studies do not establish causation. Researchers therefore designed a randomized comparative experiment. The subjects were 12 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 subject after 12 weeks, in millimeters of mercury.

An increase appears as a negative response here are the data:

Group 1 (calcium): 7 -4 18 17 -3 -5 1 10 11 -2

Group 2 (placebo); -1 12 -1 -3 3 -5 5 2 -11 -1 -3

Do the data provide sufficient evidence to conclude that a calcium supplement reduces blood pressure more than a placebo?

Carry out an appropriate test to support your answer.

??:

 ??:

Find the value for Test Statistic. 

Test Static =  

p-value =  

Step 4:   Circle one:    Reject  ?? or Fail to Reject  ??  

Conclusion in context: 

Answer 1

The Null and Alternative Hypotheses

where, is the mean decrease in systolic blood pressure in Group 1 and   is the mean decrease in systolic blood pressure in Group 2

Since the population standard deviation is not known, the t statistic will be used to compare the two groups mean hence the Two-sample t-test is used to compare the means assuming equal variance.

test statistic

The t statistic is obtained using the formula,

From the data values,

	Group 1	Group 2
Mean	5	-0.8
Std Dev	8.7433	5.9404

P-value

The P-value for the t statistic is obtained from t distribution table for the degree of freedom = n1+n2-2=18

The corresponding P-value is 0.0499 which is less than 0.05 at the 5% significance level for the one-sided alternative hypothesis. Hence, it can be concluded that the null hypothesis is rejected.