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: Exam Image Exam Image 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)

Answer 1

Answer:

t = 34.548

Step-by-step explanation:

Here  X₁ = Solid values / n

              = 26.3 +25.3+26.1+25.6+26.7+25.9/6

             =155.9 / 6

             =25.984

X₂ = Liquid values/n

    = 16.9 +16.6+16.5+17.4+17.4+17.2 / 6

    =102/6 = 17

Formula for the sample standard deviation is

$s = \sqrt {Σ(x - mean )^2/n-1}$

we get

s₁ = 0.49967

s₂ = 0.3949

Construction of hypothesis

H₀ :μ₁ = μ₂

H₁ : μ₁ ≠ μ₂

Apply test statistic formula we get the value

$t = X_{1} - X_{2} /\sqrt{S_{1}^2 /n + S_{2}^2 /n }$

putting all these values

t = 25.984 - 17 / √ (o.49967)²/6 + (0.39497)²/6

t = 34.548