Assume that you have a sample of n₁ = 6, with the sample mean X₁ = 49, and a sample standard deviation of S₁ = 6, and you have an independent sample of n₂ = 7 from another population with a sample mean of X₂ = 34 and the sample standard deviation S₂ = 5. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that H₁> H₂? Determine the hypotheses. Choose the correct answer below. OA. Ho: H1 H2 H₁: H1 H2 O C. Ho: H1>Hz H₁: H1 H2 Find the test statistic. tSTAT= (Round to two decimal places as needed.) C (B. Ho. Hi=2 H₁: H1 H₂ O D. Ho. Hi = 2 H₁: H1 H2

MATLAB: An Introduction with Applications
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Assume that you have a sample of \( n_1 = 6\), with the sample mean \(\overline{X}_1 = 49\), and a sample standard deviation of \( S_1 = 6\), and you have an independent sample of \( n_2 = 7\) from another population with a sample mean of \(\overline{X}_2 = 34\) and the sample standard deviation \( S_2 = 5\). Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that \(\mu_1 > \mu_2\)?

---

Determine the hypotheses. Choose the correct answer below.

- A. \( H_0: \mu_1 \neq \mu_2 \)  
  \( H_1: \mu_1 = \mu_2 \)

- B. \( H_0: \mu_1 \le \mu_2 \)  
  \( H_1: \mu_1 > \mu_2 \)  ✔️

- C. \( H_0: \mu_1 > \mu_2 \)  
  \( H_1: \mu_1 \le \mu_2 \)

- D. \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 \neq \mu_2 \)

Find the test statistic.

\( t_{\text{STAT}} = \) ⬜ (Round to two decimal places as needed.)
Transcribed Image Text:Assume that you have a sample of \( n_1 = 6\), with the sample mean \(\overline{X}_1 = 49\), and a sample standard deviation of \( S_1 = 6\), and you have an independent sample of \( n_2 = 7\) from another population with a sample mean of \(\overline{X}_2 = 34\) and the sample standard deviation \( S_2 = 5\). Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that \(\mu_1 > \mu_2\)? --- Determine the hypotheses. Choose the correct answer below. - A. \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - B. \( H_0: \mu_1 \le \mu_2 \) \( H_1: \mu_1 > \mu_2 \) ✔️ - C. \( H_0: \mu_1 > \mu_2 \) \( H_1: \mu_1 \le \mu_2 \) - D. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) Find the test statistic. \( t_{\text{STAT}} = \) ⬜ (Round to two decimal places as needed.)
Expert Solution
Step 1

We have given that

Sample mean (x̅1) = 49
Sample mean (x̅2) = 34
Sample size (n1) = 6
Sample size (n2) = 5
Standard deviations (s1) = 6
Standard deviations (s2) = 5
Significance level (α) = 0.01
The null and alternative hypothesis are 
H0 : µ1 ≤ µ2

H1: µ1 > µ

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