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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Statistical Hypothesis Testing Example
In this example, we have the following situation:
- **Null Hypothesis (H₀):** \( \mu_1 - \mu_2 = 0 \)
- **Alternative Hypothesis (Hₐ):** \( \mu_1 - \mu_2 \neq 0 \)
- **Significance Level (α):** 0.05
- **Sample Size 1 (n₁):** 58
- **Sample Size 2 (n₂):** 84
The question being asked is:
**What critical value forms the rejection region?**
The possible answers are:
- \( \text{t} = -1.960, \text{t} = 1.960 \)
- \( \text{t} = 1.960 \)
- \( \text{z} = -1.960, \text{z} = 1.960 \)
- \( \text{z} = -1.960 \)
To determine the correct critical value, consider whether a Z-test or a T-test is appropriate given the context of the problem and the sample sizes. The rejection region is determined based on the selected test and the significance level of 0.05 (which typically indicates a two-tailed test).](https://content.bartleby.com/qna-images/question/899c9d7f-c405-4c72-8a00-0f711d96c18e/1441f033-3245-47ff-801f-2ad136a2c525/y04n2sq_thumbnail.jpeg)
Transcribed Image Text:### Statistical Hypothesis Testing Example
In this example, we have the following situation:
- **Null Hypothesis (H₀):** \( \mu_1 - \mu_2 = 0 \)
- **Alternative Hypothesis (Hₐ):** \( \mu_1 - \mu_2 \neq 0 \)
- **Significance Level (α):** 0.05
- **Sample Size 1 (n₁):** 58
- **Sample Size 2 (n₂):** 84
The question being asked is:
**What critical value forms the rejection region?**
The possible answers are:
- \( \text{t} = -1.960, \text{t} = 1.960 \)
- \( \text{t} = 1.960 \)
- \( \text{z} = -1.960, \text{z} = 1.960 \)
- \( \text{z} = -1.960 \)
To determine the correct critical value, consider whether a Z-test or a T-test is appropriate given the context of the problem and the sample sizes. The rejection region is determined based on the selected test and the significance level of 0.05 (which typically indicates a two-tailed test).
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- A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with o = 3.0. a. Compute a 95% CI for μ when n = 25 and н x = 58.3. b. Compute a 95% CI for μ when n = 100 and x = 58.3.arrow_forwardIs there a difference among the 3 treatments in the table below? Test using α = .05 Treatment A Treatment B Treatment C 2 3 2 ∑X2 = 280 2 3 4 G = 60 3 4 5 N = 15 3 5 6 k = 3 5 5 8 SS1 = 6 SS2 = 4 SS3 = 20 What is the value of the critical F boundary? (from the tables)arrow_forward8. 1 Sa+² (1+r)v X dxarrow_forward
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