Question

A researcher wants to know if calcium is an effective treatment for lowering blood pressure. He assigns one randomly chosen group of subjects to take calcium supplements; the other group will get a placebo. At the end of the treatment period, he measures the difference in blood pressure. The 50 members of the calcium group had blood pressure lowered by an average of 25 points with standard deviation 10 points. The 50 members of the placebo group had blood pressure lowered by an average of 15 points with standard deviation 8 points. Is there evidence that calcium is an effective treatment for lowering blood pressure? State your hypotheses, the test statistic and p-value, and then write a conclusion in terms of the problem. Please show solution using Ti-83 plus

Answer 1

Let be the true average blood pressure lowered for the calcium group

be the true average blood pressure lowered for the placebo group

We want to test if there evidence that calcium is an effective treatment for lowering blood pressure, that is if the average blood pressure lowered for the calcium group is more than the average blood pressure lowered for the treatment group.

The hypotheses are

The is a test for the difference between sample means with independent samples. since the sample sizes are greater than 30, we can use normal distribution as the sampling distribution of difference in means. That is we will use 2 sample z test for means

We have the following sample information

We will estimate the population standard deviations using the sample

Set up the test on Ti-83 using

STAT+TESTS+2 sample Z test

Enter the following

Get the following

The test statistics is z=5.52

The p-value =0.0000

We will reject the null hypothesis if the p-value is less than the significance level. Assuming a 5% level of significance, we can see that the p-value is 0.0000 and it is less than the significance level 0.05. Hence we reject the null hypothesis.

We conclude that there is sufficient evidence that calcium is an effective treatment for lowering blood pressure.