need iv-vi please

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Submitted this once and they could only do i-iii, so I only need iv-vi please.

### Study of the Costa Rican Three-wattled Bellbird

**Background:**
Males of the Costa Rican three-wattled bellbird are reported to be the world's loudest birds. Their calls can be heard over half a mile away, with claims of their calls reaching 100 decibels (dB). Juanita, a Costa Rican, doubts the accuracy of this claim and decides to conduct a hypothesis test with a sample of nine adult males.

### Hypothesis Testing

**Assumptions:**
- The loudness of bellbird songs is approximately normally distributed with unknown mean (μ) and variance (σ²).

**Hypotheses:**
1. \( H_0: \mu = 100, H_A: \mu \leq 100 \)
2. \( H_0: \mu = 100, H_A: \mu < 100 \)
3. \( H_0: \mu = 100, H_A: \mu \neq 100 \)
4. \( H_0: \mu = 100, H_A: \mu > 100 \)
5. \( H_0: \mu \leq 100, H_A: \mu > 100 \)

### Results

**Data:**
- Average loudness: 94.619 dB
- Variance: 49.0001 dB²

**Tasks:**

1. **Choice of Test (ii):**
   - Conduct a hypothesis test using the data and report the p-value.
   - Decide whether to accept or reject \( H_0 \) at a 2% significance level (\( \alpha = 0.02 \)).

2. **Confidence Interval (iii):**
   - Construct a 95% confidence interval for μ.
   - Interpret the interval.

3. **Sample Size Calculation (iv):**
   - Determine the sample size required to have a margin of error of at most 5 in the confidence interval.

4. **Statistical Analysis Without Formal Training (v):**
   - Juanita assumes sample variance equals population variance.
   - Determine her p-value and decision about \( H_0 \) at the 2% significance level.

5. **Expansion of Sample Size (vi):**
   - Consider the impact of a larger sample size, say around 50, on the results.
   - Discuss why and how results may vary.

This guide provides a
Transcribed Image Text:### Study of the Costa Rican Three-wattled Bellbird **Background:** Males of the Costa Rican three-wattled bellbird are reported to be the world's loudest birds. Their calls can be heard over half a mile away, with claims of their calls reaching 100 decibels (dB). Juanita, a Costa Rican, doubts the accuracy of this claim and decides to conduct a hypothesis test with a sample of nine adult males. ### Hypothesis Testing **Assumptions:** - The loudness of bellbird songs is approximately normally distributed with unknown mean (μ) and variance (σ²). **Hypotheses:** 1. \( H_0: \mu = 100, H_A: \mu \leq 100 \) 2. \( H_0: \mu = 100, H_A: \mu < 100 \) 3. \( H_0: \mu = 100, H_A: \mu \neq 100 \) 4. \( H_0: \mu = 100, H_A: \mu > 100 \) 5. \( H_0: \mu \leq 100, H_A: \mu > 100 \) ### Results **Data:** - Average loudness: 94.619 dB - Variance: 49.0001 dB² **Tasks:** 1. **Choice of Test (ii):** - Conduct a hypothesis test using the data and report the p-value. - Decide whether to accept or reject \( H_0 \) at a 2% significance level (\( \alpha = 0.02 \)). 2. **Confidence Interval (iii):** - Construct a 95% confidence interval for μ. - Interpret the interval. 3. **Sample Size Calculation (iv):** - Determine the sample size required to have a margin of error of at most 5 in the confidence interval. 4. **Statistical Analysis Without Formal Training (v):** - Juanita assumes sample variance equals population variance. - Determine her p-value and decision about \( H_0 \) at the 2% significance level. 5. **Expansion of Sample Size (vi):** - Consider the impact of a larger sample size, say around 50, on the results. - Discuss why and how results may vary. This guide provides a
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