Math  /  Data & Statistics

QuestionHypothesis Question 3, 9.5.59 HW Score: 17.14%,1.7117.14 \%, 1.71 of 10 points of Two Means Part 7 of 7 Points: 0 of 1 Save
Triglycerides 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 . (i) Click the icon to view the Minitab outputs.
Find the test statistic for this test. t=2.60\mathrm{t}=-2.60 (Type an integer or a decimal.) Find the p-value for this test. pp-value =0.006=0.006 (Type an integer or a decimal.) What is the conclusion for this test? A. Do not reject H0\mathrm{H}_{0}. Men have a significantly higher mean triglyceride level than women. B. Do not reject H0\mathrm{H}_{0}. Men do not have a significantly higher mean triglyceride level than women. C. Reject H0\mathrm{H}_{0}. Men do not have a significantly higher mean triglyceride level than women. D. Reject H0H_{0}. Men have a significantly higher mean triglyceride level than women. Clear all Chack answar

Studdy Solution

STEP 1

What is this asking? Do men have higher triglyceride levels than women, and what's the proof? Watch out! Don't mix up the sample means with what the hypothesis test is actually telling us!
Also, make sure to pick the right Minitab output and interpret the p-value correctly.

STEP 2

1. Check the sample means.
2. State the hypotheses.
3. Interpret the provided test statistic and p-value.
4. Draw a conclusion.

STEP 3

The problem says to refer to some Minitab output (figure A, not provided here) to find the sample means and which group has a higher sample mean.
Let's assume that figure A shows that men have a higher sample mean triglyceride level than women.
We'll need this later!

STEP 4

We're testing if men have a *higher* mean triglyceride level than women.
Let μM\mu_M be the mean triglyceride level for men and μW\mu_W be the mean triglyceride level for women.

STEP 5

Our **null hypothesis** (H0H_0) is that there's no difference, or that men have a lower or equal mean: μMμW\mu_M \le \mu_W.

STEP 6

Our **alternative hypothesis** (HaH_a) is what we're trying to prove: that men have a higher mean: μM>μW\mu_M > \mu_W.
This is a **one-tailed test** since we're only interested in whether men have *higher* levels.

STEP 7

We're given a **test statistic** of t=2.60t = -2.60.
This seems odd since we're testing if men have *higher* levels, but we have a *negative* t-value.
This is because the Minitab output likely calculated the difference as women minus men.
Since our alternative hypothesis is that men have higher levels, a negative t-value is evidence *against* the alternative hypothesis.

STEP 8

The **p-value** is given as 0.0060.006.
This means that if there were *actually no difference* in triglyceride levels between men and women (or if women had higher levels), there's only a 0.006\textbf{0.006} (or \textbf{0.6%}) chance of observing a sample difference as extreme as the one we saw (or even more extreme).
That's a tiny chance!

STEP 9

Our **significance level** is 0.05\textbf{0.05} (or \textbf{5%}).
Since our p-value (0.0060.006) is *less than* our significance level (0.050.05), we **reject the null hypothesis**!

STEP 10

Rejecting the null hypothesis means we have enough evidence to support the alternative hypothesis.
However, remember the negative t-value!
It means that the sample mean for women was actually *higher* than for men.
This contradicts the problem statement that says men have a higher sample mean, so something is off.
The provided test statistic and p-value do not match the problem description.

STEP 11

Based on the given p-value (0.0060.006) being less than the significance level (0.050.05), we reject the null hypothesis.
However, the negative t-value indicates the sample mean for women was higher, contradicting the problem statement.
Therefore, there appears to be an inconsistency in the provided data.
Assuming the p-value and t-statistic are correct, the correct answer would be C.
Reject H0H_0.
Men do *not* have a significantly higher mean triglyceride level than women.

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