Which one of the following is not a condition for inference comparing two means? independent simple random samples from two populations populations must be distinct both populations are Normally distributed the two sample sizes must be equal

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**Question:** Which one of the following is not a condition for inference comparing two means?

- ○ independent simple random samples from two populations
- ○ populations must be distinct
- ○ both populations are Normally distributed
- ● the two sample sizes must be equal

**Explanation:**
The highlighted answer indicates that "the two sample sizes must be equal" is not a condition for inference when comparing two means. The other conditions listed are generally required when performing such statistical analyses.
Transcribed Image Text:**Question:** Which one of the following is not a condition for inference comparing two means? - ○ independent simple random samples from two populations - ○ populations must be distinct - ○ both populations are Normally distributed - ● the two sample sizes must be equal **Explanation:** The highlighted answer indicates that "the two sample sizes must be equal" is not a condition for inference when comparing two means. The other conditions listed are generally required when performing such statistical analyses.
Two independent samples from normal distributions are being compared. The sample data are summarized in the table.

| Population | Population mean | Sample size | Sample mean | Sample standard deviation | Standard error estimate |
|------------|------------------|-------------|-------------|------------------------|-------------------------|
| 1          | μ₁ (unknown)     | n₁ = 15     | x̄₁ = 12.6  | s₁ = 2.500             | SE₁ = 0.645             |
| 2          | μ₂ (unknown)     | n₂ = 13     | x̄₂ = 10.5  | s₂ = 2.260             | SE₂ = 0.627             |

The estimated standard error of the difference of the two sample means is SE = 0.900.

Compute the value of the two-sample t-statistic used to test the null hypothesis H₀: μ₁ = μ₂. Please give your answer precise to three decimal places.

t = [ ]
Transcribed Image Text:Two independent samples from normal distributions are being compared. The sample data are summarized in the table. | Population | Population mean | Sample size | Sample mean | Sample standard deviation | Standard error estimate | |------------|------------------|-------------|-------------|------------------------|-------------------------| | 1 | μ₁ (unknown) | n₁ = 15 | x̄₁ = 12.6 | s₁ = 2.500 | SE₁ = 0.645 | | 2 | μ₂ (unknown) | n₂ = 13 | x̄₂ = 10.5 | s₂ = 2.260 | SE₂ = 0.627 | The estimated standard error of the difference of the two sample means is SE = 0.900. Compute the value of the two-sample t-statistic used to test the null hypothesis H₀: μ₁ = μ₂. Please give your answer precise to three decimal places. t = [ ]
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