A crossover trial to measure the effect of fruit and vegetable intake on systoli

Question

A crossover trial to measure the effect of fruit and vegetable intake on systolic blood pressure (SBP) is performed on 50 individuals. All 50 people in the sample are instructed to not eat any fruits or vegetables for 6 weeks (probably not ethical) at which point their SBP measurements are recorded. Next participants are instructed to eat 5 or more servings of fruits and vegetables every day for 6 weeks, then SBP measurements are taken again. Among these 50 people, the mean SBP difference was -8.9 and the standard deviation was 16.4. Compute the proper test statistic to find if there is a statistically significant difference in mean SBP measured 6 weeks apart.

Explanation / Answer

This accounts for a paired-t test.

Hypotheses:

H0: mud=0 (There is no difference in mean SBP before and after consumption of fruits and vegetables)

H1: mud not equal to 0 (There is difference in mean SBP before and after consumption of fruits and vegetables)

Assumptions: Assume that paired-data collection, Independence assumption, Randomization condition and Neraly normal condition are reasonable met.

Test: Use student's t model with 50-1=49 df.

From information,

n=50, dbar=-8.9, sd=16.4

SE(dbar)=sd/sqrt n=16.4/sqrt 50=2.32

t49=(dbar-0)/SE(dbar)=-8.9-0/2.32=-3.84

The p value is 0.0001

Conclusion: The p value is less than alpha=0.05. Reject null hypothesis to claim that there is significant difference in SBP before and after consumption of fruits and vegetables.

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