Mathematics, 26.11.2019 07:31 firefightergros3547

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: [26.2,25.6,25.5,26.1,26.5,26.7] liquid: [16.3,16.4,16.3,16.7,16.6,17.7] 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?

Answers: 1

Show answers

Answers

Answer from: steven0448

t= 32.327

Would be a significant difference in the average amount of saturated fat in solid and liquid fats.

Step-by-step explanation:

1) Data given and notation

Stick:[26.2,25.6,25.5,26.1,26.5,26.7]

Liquid:[16.3,16.4,16.3,16.7,16.6,17.7]

$\bar X_{stick}$ represent the mean for the sample Stick

$\bar X_{Liquid}$ represent the mean for the sample Liquid

$s_{stick}$ represent the sample standard deviation for the sample Stick

$s_{Liquid}$ represent the sample standard deviation for the sample Liquid

$n_{stick}=6$ sample size for the group Stick

$n_{Liquid}=6$ sample size for the group Liquid

t would represent the statistic (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

Null Hypothesis : $\mu_{stick}=\mu_{Liquid}$

Alternative Hypothesis : $\mu_{stick} \neq \mu_{Liquid}$

If we analyze the size for the samples both are < 30 so for this case we can apply a t test to compare means, and the statistic formula is:

$t=\frac{\bar X_{stick}-\bar X_{Liquid}}{\sqrt{\frac{s^2_{stick}}{n_{stick}}+\frac{s^2_{Liquid}}{n_{Liquid}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

3) Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

$\bar X_{stick}=26.10$ $s_{stick}=0.477$

$\bar X_{Liquid}=16.67$ $s_{Liquid}=0.532$

And with this we can replace in formula (1) like this:

$t=\frac{26.10-16.67}{\sqrt{\frac{0.477^2}{6}+\frac{0.532^2}{6}}}}=32.327$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

$df=n_{stick}+n_{liquid}-2=6+6-2=10$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{(10)}32.327)=1.8x10^{-11}$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and a would be a significant difference in the average amount of saturated fat in solid and liquid fats.

Answer from: Quest

i just took the test, the correct answer is .. 31.5 in.

Answer from: Quest

6/20

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:10

The green family is a family of six people. they have used 4,885.78 gallons of water so far this month. they cannot exceed 9,750.05 gallons per month during drought season. write an inequality to show how much water just one member of the family can use for the remainder of the month, assuming each family member uses the same amount of water every month.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Someone answer asap for ! a ball is rolled down a ramp. the height, f(x), in meters, of the ball x seconds after it is released is modeled by the function f(x) = x²- 10x + 25 for all values of x from 0 to 5. which statement about the ball is true? a. the maximum height of the ball is 5 meters b. the height of the ball increases from 0 to 5 meters above the ground. c. the ball has traveled 5 meters when it reaches the bottom of the ramp. d. the ball has been traveling for 5 seconds when it reaches the bottom of the ramp

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

An electrician cuts a 136 foot long piece of cable. one piece is 16 feet less than 3 times the length of the other piece. find the length of each piece

Answers: 1

Answer

You know the right answer?

Solid fats are more likely to raise blood cholesterol levels than liquid fats. suppose a nutritionis...

Questions