of # o} $1 = 0.75; s2 = 0.71 E = 34.08 ; z2 = 34.32 %3D %3D n1 = 23 ; n2 = 32 %3! a. Calculate the Standard Error si,-i, = (use 3 decimal places) b. Calculate the t-test statistic using the standard error from part a. t = (use 2 decimal places) c. What are the degrees of freedom? df %3D

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**Testing the Claim \( \mu_1 < \mu_2 \): A Step-by-Step Guide**

Assume the samples are normally distributed, random, and independent.

### Given Data:

\[
\sigma_1^2 \neq \sigma_2^2
\]

\( s_1 = 0.75; \, s_2 = 0.71 \)

\( \bar{x}_1 = 34.08; \, \bar{x}_2 = 34.32 \)

\( n_1 = 23; \, n_2 = 32 \)

### Steps:

**a. Calculate the Standard Error \( s_{\bar{x}_1 - \bar{x}_2} \):**

- Fill in the box (use 3 decimal places).

**b. Calculate the t-test statistic using the standard error from part a. \( t = \):**

- Fill in the box (use 2 decimal places).

**c. What are the degrees of freedom? \( df = \):**

- Fill in the box.

**d. At \( \alpha = 0.10 \). Use the distribution table to find the critical values for the rejection region. \( t_c = \):**

- Fill in the box (use 4 decimal places).

**e. Conclusion:**

What is your conclusion?

- Reject the null hypothesis and support the claim
- Accept the alternative hypothesis and reject the claim
- Accept the null hypothesis and support the claim
- Fail to reject the null hypothesis and do not support the claim
- Reject the alternative hypothesis and support the claim

Follow these steps to solve the hypothesis test and make an appropriate conclusion based on the statistical evidence.
Transcribed Image Text:**Testing the Claim \( \mu_1 < \mu_2 \): A Step-by-Step Guide** Assume the samples are normally distributed, random, and independent. ### Given Data: \[ \sigma_1^2 \neq \sigma_2^2 \] \( s_1 = 0.75; \, s_2 = 0.71 \) \( \bar{x}_1 = 34.08; \, \bar{x}_2 = 34.32 \) \( n_1 = 23; \, n_2 = 32 \) ### Steps: **a. Calculate the Standard Error \( s_{\bar{x}_1 - \bar{x}_2} \):** - Fill in the box (use 3 decimal places). **b. Calculate the t-test statistic using the standard error from part a. \( t = \):** - Fill in the box (use 2 decimal places). **c. What are the degrees of freedom? \( df = \):** - Fill in the box. **d. At \( \alpha = 0.10 \). Use the distribution table to find the critical values for the rejection region. \( t_c = \):** - Fill in the box (use 4 decimal places). **e. Conclusion:** What is your conclusion? - Reject the null hypothesis and support the claim - Accept the alternative hypothesis and reject the claim - Accept the null hypothesis and support the claim - Fail to reject the null hypothesis and do not support the claim - Reject the alternative hypothesis and support the claim Follow these steps to solve the hypothesis test and make an appropriate conclusion based on the statistical evidence.
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