Question

A researcher wishes to investigate the idea that eating sea salt raises blood pressure less than eating normal table salt. He randomly selects two groups, each with 13 people. He arranges that Group 1 will be on a high sea salt diet for 2 weeks, while Group 2 will be on a high table salt diet. He measures their blood pressure after the two weeks. The mean systolic blood pressure for Group 1, x¯1x¯1, is found to be 126 with a sample standard deviation of 4.0, while for Group 2 the mean, x¯2x¯2 is found to be 116 with a sample standard deviation of 3.7. Suppose the null hypothesis is that x¯1=x¯2x¯1=x¯2. Calculate the appropriate statistic to investigate whether the null hypothesis is likely to be valid.

Answer 1

Here, two different groups are used to collect data in two different situations. Further we do not know population standard deviation (or variance). So, we have to perform two sample t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

First sample size

Second sample size

Degrees of freedom

[Using R-code 'pt(6.617083,24)']

We reject our null hypothesis if ,level of significance.

We generally test for level of significance 0.10, 0.05, 0.01 or something like these.

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant evidence that eating sea salt raises blood pressure less than eating normal table salt.