Questions: 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. Minitab Output (A) Gender N Mean StDev SE Mean Female 43 85.5 34.6 5.3 Male 49 117.6 54.4 7.8 Difference =mu (Female) -mu (Male) Estimate for difference: - 32.1 95% CI for difference: (-50.8,-13.4) C: T-Test of difference =0(vs>): T-Value =-3.42 P-value =1.000 D: T-Test of difference =0 (vs >): T-Value =-3.42 P-value =0.001

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. Minitab Output (A) Gender N Mean StDev SE Mean Female 43 85.5 34.6 5.3 Male 49 117.6 54.4 7.8 Difference =mu (Female) -mu (Male) Estimate for difference: - 32.1 95% CI for difference: (-50.8,-13.4) C: T-Test of difference =0(vs>): T-Value =-3.42 P-value =1.000 D: T-Test of difference =0 (vs >): T-Value =-3.42 P-value =0.001
Transcript text: 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. Minitab Output (A) \begin{tabular}{|c|c|c|c|c|} \hline \multirow[t]{2}{*}{(A)} & \multicolumn{4}{|l|}{\multirow[b]{2}{*}{Two-sample T-Test and CI: Triglycerides, Gender}} \\ \hline & & & & \\ \hline Gender & N & Mean & StDev & SE Mean \\ \hline Female & 43 & 85.5 & 34.6 & 5.3 \\ \hline Male & 49 & 117.6 & 54.4 & 7.8 \\ \hline \multicolumn{5}{|l|}{Difference $=\mathrm{mu}$ (Female) -mu (Male)} \\ \hline \multicolumn{5}{|l|}{Estimate for difference: - 32.1} \\ \hline \multicolumn{5}{|l|}{95\% Cl for difference: $(-50.8,-13.4)$} \\ \hline \end{tabular} C: T-Test of difference $=0(\mathrm{vs}>):$ T-Value $=-3.42 \quad$ P-value $=1.000$ D: T-Test of difference $=0$ (vs $>$): T-Value $=-3.42 \quad$ P-value $=0.001$
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Solution

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Solution Steps

Step 1: Sample Means

The sample means for triglyceride levels are calculated as follows:

  • For females: \[ \bar{x}_1 = 85.5 \]
  • For males: \[ \bar{x}_2 = 117.6 \]

Comparing the two means, we find that: \[ \bar{x}_2 > \bar{x}_1 \implies \text{Males have a higher sample mean triglyceride level.} \]

Step 2: Standard Error Calculation

The standard error \( SE \) is calculated using the formula: \[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{0.0}{43} + \frac{0.0}{49}} = 0.0 \]

Step 3: Test Statistic Calculation

The test statistic \( t \) is calculated as: \[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{85.5 - 117.6}{0.0} = -1.5649679639180138 \times 10^{16} \]

Step 4: Degrees of Freedom

The degrees of freedom \( df \) are calculated using the formula: \[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{0.0}{0.0} = 48.0 \]

Step 5: P-Value Calculation

The p-value associated with the test statistic is: \[ P = T(t) = T(-1.5649679639180138 \times 10^{16}) = 0.0 \]

Step 6: Hypothesis Testing

At a significance level of \( \alpha = 0.05 \), we compare the p-value to \( \alpha \): \[ P < \alpha \implies \text{Reject the null hypothesis.} \] This indicates that there is sufficient evidence to conclude that men have a higher mean triglyceride level than women.

Final Answer

\[ \boxed{\text{Males have a higher mean triglyceride level than females.}} \]

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