Math / Data & Statistics

QuestionStudent/PlayerTest.aspx?canvas_workflow_statesavailable\&canvas_enrollment_state=active\&canvas_user_id=3490178canvas_module_id=9590348canvas_assignment_points kriscia mejia Question 1 of 5 This test: 20 point(s) possible This question: 4 point(s) possible Submit test ven in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally tributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. c. $H_{0}: \mu_{1}=\mu_{2}$ \begin{tabular}{|c|c|c|} \hline & Male BMI & Female BMI \\ \hline $\boldsymbol{\mu}$ & $\mu_{1}$ & $\mu_{2}$ \\ \hline $\boldsymbol{n}$ & 49 & 49 \\ \hline $\bar{x}$ & 27.8756 & 26.0709 \\ \hline $s$ & 8.866451 & 4.146108 \\ \hline \end{tabular} $H_{1}: \mu_{1}>\mu_{2}$ D. $H_{0}: \mu_{1} \gtrless \mu_{2}$ $H_{1}: \mu_{1}<\mu_{2}$ est statistic, $t_{\text {t }}$ is 1.29 . (Round to two decimal places as needed.) -value is 0.202 . (Round to three decimal places as needed.) the conclusion for the test.
Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. eject the null hypothesis. There is sufficient evidence to warrant reje tejection of the claim that men and women have the same mean BMI. of the claim that men and women have the salme mean BMI. $-\mu_{2}<\Pi$

Studdy Solution

STEP 1

1. The samples are independent simple random samples.
2. The populations are normally distributed.
3. The population standard deviations are not assumed to be equal.
4. A significance level of $\alpha = 0.05$ is used.

STEP 2

1. Identify the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. Make a decision based on the p-value and significance level.
4. State the conclusion.

STEP 3

Identify the null and alternative hypotheses:
- Null hypothesis ( $H_0$ ): $\mu_1 = \mu_2$ - Alternative hypothesis ( $H_1$ ): $\mu_1 > \mu_2$

STEP 4

The test statistic $t_{\text{t}}$ is given as 1.29, and the p-value is given as 0.202.

STEP 5

Compare the p-value to the significance level:
- Significance level ( $\alpha$ ): 0.05 - P-value: 0.202
Since the p-value (0.202) is greater than the significance level (0.05), we fail to reject the null hypothesis.

STEP 6

State the conclusion:
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

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Studdy Solution

STEP 1

1. The samples are independent simple random samples.
2. The populations are normally distributed.
3. The population standard deviations are not assumed to be equal.
4. A significance level of $\alpha = 0.05$ is used.

STEP 2

1. Identify the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. Make a decision based on the p-value and significance level.
4. State the conclusion.

STEP 3

Identify the null and alternative hypotheses:
- Null hypothesis ( $H_0$ ): $\mu_1 = \mu_2$ - Alternative hypothesis ( $H_1$ ): $\mu_1 > \mu_2$

STEP 4

The test statistic $t_{\text{t}}$ is given as 1.29, and the p-value is given as 0.202.

STEP 5

Compare the p-value to the significance level:
- Significance level ( $\alpha$ ): 0.05 - P-value: 0.202
Since the p-value (0.202) is greater than the significance level (0.05), we fail to reject the null hypothesis.

STEP 6

State the conclusion:
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

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Studdy Solution

STEP 1

1. The samples are independent simple random samples.2. The populations are normally distributed.3. The population standard deviations are not assumed to be equal.4. A significance level of α=0.05 \alpha = 0.05 α=0.05 is used.

STEP 2

1. Identify the null and alternative hypotheses.2. Calculate the test statistic and p-value.3. Make a decision based on the p-value and significance level.4. State the conclusion.

STEP 3

Identify the null and alternative hypotheses:- Null hypothesis (H0 H_0 H0​): μ1=μ2 \mu_1 = \mu_2 μ1​=μ2​ - Alternative hypothesis (H1 H_1 H1​): μ1>μ2 \mu_1 > \mu_2 μ1​>μ2​

STEP 4

The test statistic tt t_{\text{t}} tt​ is given as 1.29, and the p-value is given as 0.202.

STEP 5

Compare the p-value to the significance level:- Significance level (α \alpha α): 0.05 - P-value: 0.202Since the p-value (0.202) is greater than the significance level (0.05), we fail to reject the null hypothesis.

STEP 6

State the conclusion:Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

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

1. The samples are independent simple random samples.
2. The populations are normally distributed.
3. The population standard deviations are not assumed to be equal.
4. A significance level of $\alpha = 0.05$ is used.

1. Identify the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. Make a decision based on the p-value and significance level.
4. State the conclusion.

Identify the null and alternative hypotheses:
- Null hypothesis ( $H_0$ ): $\mu_1 = \mu_2$ - Alternative hypothesis ( $H_1$ ): $\mu_1 > \mu_2$

The test statistic $t_{\text{t}}$ is given as 1.29, and the p-value is given as 0.202.

Compare the p-value to the significance level:
- Significance level ( $\alpha$ ): 0.05 - P-value: 0.202
Since the p-value (0.202) is greater than the significance level (0.05), we fail to reject the null hypothesis.

State the conclusion:
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.