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 12 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¯1, is found to be 133 with a sample standard deviation of 3.1, while for Group 2 the mean, x¯2 is found to be 118 with a sample standard deviation of 4.0. Suppose the null hypothesis is that x¯1=x¯2. Calculate the appropriate statistic to investigate whether the null hypothesis is likely to be valid.

Answer 1

The hypothesis is:

H0: Blood pressure remains same for both the consumption of sea salt and table salt; x1 = x2

H1: Blood pressure raises by consumption of table salt more than the consumption of sea salt; x1 < x2

The test statostic under the null hypothesis is:

t = [ (x1 - x2) - d ] / SE

where SE = sqrt[ (s12/n1) + (s22/n2) ] =

and DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } = 20.71 ~ 21

t = -10.26779

Incase we had an alternative hypothesis that x1 not equal to x2 or x1 greater than x2 then the null hypothesis would be rejected.

However for X1<X2 we may need to accept the null hypothesis at 5% level of significance and conclude that the blood pressure may be same from consumption of both the salts.

( Kindly check the values of x1 and x2 since they seem interchangable and will have a p-value 0.0000000006 which will lead to the rejection of the null hypothesis at 5% level of significance.)