Math / Data & Statistics

QuestionTriglycerides are a form of fat found in the body. Using data from a certain organization, determine whether men have higher triglyceride levels than women. a. Report the sample means and state which group had the higher sample mean triglyceride level. Refer to the Minitab output in figure (A). b. Carry out a hypothesis test to determine whether men have a higher mean triglyceride level than women. Assume that all necessary conditions for carrying out a hypothesis test hold. Refer to the Minitab output provided in figure (A). Output for three different alternative hypotheses is provided-see figures (B), (C), and (D)-and you must choose and state the most appropriate output. Use a significance level of 0.05 a. The sample mean for the women was $\square$ . (Type an integer or a decimal.)
Minitab Output (A) (B)
B: T-Test of difference $=0($ vs $<$ ); T-Value $=-2.60 \quad P$ -value $=0.006$ (C)
C: T-Test of difference $=0($ vs $>):$ T-Value $=-2.60 \quad P$ -value $=0.994$ (D)
D: T-Test of difference $=0($ vs $\neq)$ : T-Value $=-2.60 \quad$ P-value $=0.011$ Clear all Check answer

Studdy Solution

STEP 1

What is this asking? Do men have higher triglyceride levels than women, and can we prove it statistically? Watch out! Don't mix up the means for men and women, and make sure you pick the right hypothesis test!
Also, understand why we're doing each step.

STEP 2

1. Find the sample means.
2. State which group has the higher sample mean.
3. Select the correct hypothesis test.
4. Interpret the results.

STEP 3

Alright, let's locate those sample means!
The problem gives us the Minitab output, which shows the sample mean for women is $84.3$ and for men it's $114.1$ .

STEP 4

Comparing the means, we see that $114.1$ is greater than $84.3$ .
So, men have the higher sample mean triglyceride level.

STEP 5

We're testing if men have a higher mean triglyceride level than women.
This means we're looking for a one-tailed test where the alternative hypothesis is that the difference (women minus men) is less than zero.
That's because if men have higher levels, subtracting the men's mean from the women's mean will result in a negative number.

STEP 6

Looking at the Minitab output, option (B) is the one we need: "T-Test of difference $= 0$ (vs $<$ )".
This corresponds to our alternative hypothesis.
Options (C) and (D) test for a greater than or not-equal-to relationship, which isn't what we're looking for.

STEP 7

The output for option (B) gives us a T-value of $-2.60$ and a P-value of $0.006$ .
Since our significance level is $0.05$ , and our P-value ( $0.006$ ) is less than $0.05$ , we reject the null hypothesis.

STEP 8

This means there's strong evidence to suggest that men do have a higher mean triglyceride level than women!

STEP 9

The sample mean for women is 84.3.
Men have the higher sample mean.
Using the results from the T-test (option B), we reject the null hypothesis and conclude that men have a statistically significantly higher mean triglyceride level than women.

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Studdy Solution

STEP 1

What is this asking? Do men have higher triglyceride levels than women, and can we prove it statistically? Watch out! Don't mix up the means for men and women, and make sure you pick the right hypothesis test!
Also, understand why we're doing each step.

STEP 2

1. Find the sample means.
2. State which group has the higher sample mean.
3. Select the correct hypothesis test.
4. Interpret the results.

STEP 3

Alright, let's locate those sample means!
The problem gives us the Minitab output, which shows the sample mean for women is $84.3$ and for men it's $114.1$ .

STEP 4

Comparing the means, we see that $114.1$ is greater than $84.3$ .
So, men have the higher sample mean triglyceride level.

STEP 5

STEP 6

Looking at the Minitab output, option (B) is the one we need: "T-Test of difference $= 0$ (vs $<$ )".
This corresponds to our alternative hypothesis.
Options (C) and (D) test for a greater than or not-equal-to relationship, which isn't what we're looking for.

STEP 7

The output for option (B) gives us a T-value of $-2.60$ and a P-value of $0.006$ .
Since our significance level is $0.05$ , and our P-value ( $0.006$ ) is less than $0.05$ , we reject the null hypothesis.

STEP 8

This means there's strong evidence to suggest that men do have a higher mean triglyceride level than women!

STEP 9

The sample mean for women is 84.3.
Men have the higher sample mean.
Using the results from the T-test (option B), we reject the null hypothesis and conclude that men have a statistically significantly higher mean triglyceride level than women.

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Studdy Solution

STEP 1

What is this asking? Do men have higher triglyceride levels than women, and can we prove it statistically? Watch out! Don't mix up the means for men and women, and make sure you pick the right hypothesis test!Also, understand *why* we're doing each step.

STEP 2

1. Find the sample means.2. State which group has the higher sample mean.3. Select the correct hypothesis test.4. Interpret the results.

STEP 3

Alright, let's **locate** those sample means!The problem gives us the Minitab output, which shows the **sample mean** for women is 84.384.384.3 and for men it's 114.1114.1114.1.

STEP 4

Comparing the **means**, we see that 114.1114.1114.1 is **greater** than 84.384.384.3.So, men have the higher sample mean triglyceride level.

STEP 5

STEP 6

Looking at the Minitab output, option (B) is the one we need: "T-Test of difference =0= 0=0 (vs <<<)".This corresponds to our **alternative hypothesis**.Options (C) and (D) test for a greater than or not-equal-to relationship, which isn't what we're looking for.

STEP 7

The output for option (B) gives us a **T-value** of −2.60-2.60−2.60 and a **P-value** of 0.0060.0060.006.Since our **significance level** is 0.050.050.05, and our **P-value** (0.0060.0060.006) is *less than* 0.050.050.05, we **reject the null hypothesis**.

STEP 8

This means there's **strong evidence** to suggest that men *do* have a higher mean triglyceride level than women!

STEP 9

The sample mean for women is **84.3**.Men have the higher sample mean.Using the results from the T-test (option B), we reject the null hypothesis and conclude that men have a statistically significantly higher mean triglyceride level than women.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Do men have higher triglyceride levels than women, and can we prove it statistically? Watch out! Don't mix up the means for men and women, and make sure you pick the right hypothesis test!
Also, understand why we're doing each step.

1. Find the sample means.
2. State which group has the higher sample mean.
3. Select the correct hypothesis test.
4. Interpret the results.

Alright, let's locate those sample means!
The problem gives us the Minitab output, which shows the sample mean for women is $84.3$ and for men it's $114.1$ .

Comparing the means, we see that $114.1$ is greater than $84.3$ .
So, men have the higher sample mean triglyceride level.

Looking at the Minitab output, option (B) is the one we need: "T-Test of difference $= 0$ (vs $<$ )".
This corresponds to our alternative hypothesis.
Options (C) and (D) test for a greater than or not-equal-to relationship, which isn't what we're looking for.

The output for option (B) gives us a T-value of $-2.60$ and a P-value of $0.006$ .
Since our significance level is $0.05$ , and our P-value ( $0.006$ ) is less than $0.05$ , we reject the null hypothesis.

This means there's strong evidence to suggest that men do have a higher mean triglyceride level than women!

The sample mean for women is 84.3.
Men have the higher sample mean.
Using the results from the T-test (option B), we reject the null hypothesis and conclude that men have a statistically significantly higher mean triglyceride level than women.