Solid fats are more likely to raise blood cholesterol levels than liquid fats. S

Question

Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)

Explanation / Answer

H_0: mstick = mliquid

H_1: mstick not equal to mliquid

stick = c(25.5,26.7,26.5,26.6,26.3,26.4)
liquid = c(16.5,17.1,17.5,17.3,17.2,16.7)
mstick = mean(stick)
mliquid = mean(liquid)
ssstick =(6-1)*var(stick)
ssliquid = (6-1)*var(liquid)
Ssquar = (ssstick+ssliquid)/(6+6-2)
t_est=(mstick-mliquid)/sqrt((Ssquar/6)+(Ssquar/6)) = 39.60427
tvalue = qt(p = 0.05/2,df =6+6-2,lower.tail = TRUE) =  -2.228139 = 2.228139(symmetryt of t distribution)

so we can reject H_0
Pvalue = pt(q = t_est, df = 6+6-2, lower.tail = false) =1.258923e-12 <0.025.

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