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:
Stick= [25.5, 26.7, 26.5, 26.6, 26.3, 26.4]
Liquid= [16.5, 17.1, 17.5, 17.3, 17.2, 16.7]
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)
a. t = 25.263
b. z = 39.604
c. t = 39.604
d. t = 39.104
e. z = 39.104

Step-by-step explanation:

We would determine the mean and standard deviation for the stick and liquid fats.

Mean = sum of items/number of I teams

For the stick margarine,

n = 6

Mean = (25.5 + 26.7 + 26.5 + 26.6 + 26.3 + 26.4)/6 = 26.3

Standard deviation, s1 = √(summation(x - mean)^2/n

Summation(x - mean)^2 = (25.5 - 26.3)^2 + (26.7 - 26.3)^2 + (26.5 - 26.3)^2 + (26.6 - 26.3)^2 + (26.3 - 26.3)^2 + (26.4 - 26.3)^2 = 0.94

s1 = √0.94/6 = 0.41

For liquid margarine,

n = 6

Mean = (16.5 + 17.1 + 17.5 + 17.3 + 17.2 + 16.7)/6 = 17.1

Summation(x - mean)^2 = (16.5 - 17.1)^2 + (17.1 - 17.1)^2 + (17.5 - 17.1)^2 + (17.3 - 17.1)^2 + (17.2 - 17.1)^2 + (16.7 - 17.1)^2 = 0.73

s2 = √0.73/6 = 0.4

Since we know the sample standard deviation and the sample sizes are small, we would determine the t test statistic by applying the formula,

(x1 - x2)/√(s1²/n1 + s2²/n2)

x1 and x2 are the sample means

Therefore,

t = (26.3 - 17.1)/√(0.41²/6 + 0.4²/6)

t = 39.34

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.