Suppose we are conducting the following hypothesis test at the 10% significance level. HO: µ1 - µ2 = 0 Ha: µ1 - µ2 < 0 Assume equal population variances. If n1 = 9 and n2 = 7, what critical value forms the rejection region? %3D Ot=-1.345 O z = 1.28 Ot= 1.345 O z = -1.28

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### Conducting a Hypothesis Test at the 10% Significance Level

Suppose we are conducting the following hypothesis test at the 10% significance level:

- **Null Hypothesis (H0)**: μ₁ - μ₂ = 0
- **Alternative Hypothesis (Ha)**: μ₁ - μ₂ < 0

Assume equal population variances.

Given:
- Sample size for the first sample (n₁) = 9
- Sample size for the second sample (n₂) = 7

**Question**: What critical value forms the rejection region?

**Options**:
- \( t = -1.345 \)
- \( z = 1.28 \)
- \( t = 1.345 \)
- \( z = -1.28 \)

To identify the correct critical value for the rejection region, we need to consider the appropriate t-distribution or z-distribution for the given significance level, sample sizes, and alternative hypothesis.

In hypothesis testing, the rejection region is determined based on the calculated critical value which, in this context, is set by the lower tail of the distribution because the alternative hypothesis is a one-tailed test (μ₁ - μ₂ < 0).
Transcribed Image Text:### Conducting a Hypothesis Test at the 10% Significance Level Suppose we are conducting the following hypothesis test at the 10% significance level: - **Null Hypothesis (H0)**: μ₁ - μ₂ = 0 - **Alternative Hypothesis (Ha)**: μ₁ - μ₂ < 0 Assume equal population variances. Given: - Sample size for the first sample (n₁) = 9 - Sample size for the second sample (n₂) = 7 **Question**: What critical value forms the rejection region? **Options**: - \( t = -1.345 \) - \( z = 1.28 \) - \( t = 1.345 \) - \( z = -1.28 \) To identify the correct critical value for the rejection region, we need to consider the appropriate t-distribution or z-distribution for the given significance level, sample sizes, and alternative hypothesis. In hypothesis testing, the rejection region is determined based on the calculated critical value which, in this context, is set by the lower tail of the distribution because the alternative hypothesis is a one-tailed test (μ₁ - μ₂ < 0).
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