last two ### Hypothesis Testing of Costa Rican Three-wattled Bellbird Loudness**Context:**Males of the Costa Rican three-wattled bellbird are considered the loudest birds globally. Their call, reaching an audience over half a mile away, is claimed to reach 100 dB (decibels), comparable to a live rock concert. Juanita, skeptical of such claims, aims to verify this through statistical analysis using a sample of 9 bellbirds.**Assumptions:**- The loudness of bellbird songs is approximately normally distributed with mean μ (in dB) and unknown variance σ² (in dB²).**Tasks:**1. **Hypotheses Formulation (i):** Juanita needs to select the appropriate null (H₀) and alternative hypotheses (Hₐ) from the following options: - H₀: μ = 100, Hₐ: μ ≠ 100 - H₀: μ = 100, Hₐ: μ < 100 - H₀: μ = 100, Hₐ: μ > 1002. **Conducting the Test (ii):** - Sample results: Average loudness = 94.619 dB, Variance = 49.0001 dB². - Conduct a hypothesis test to choose between the hypotheses, reporting the p-value and decision at a 2% significance level (α = 0.02).3. **95% Confidence Interval (iii):** - Construct a 95% confidence interval for μ and provide an interpretation.4. **Sample Size Calculation (iii, second part):** - Determine necessary sample size for a margin of error not exceeding 5 dB within the 95% confidence interval.5. **P-value Interpretation (iv):** - Despite lacking statistical training, Juanita adopts population variance as sample variance. Determine her p-value and decide whether she accepts or rejects H₀ at the established significance level (2%).This educational exercise demonstrates hypothesis testing and statistical interpretation through analyzing the bellbird's loudness claims.

Name: last two ### Hypothesis Testing of Costa Rican Three-wattled Bellbird
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: last two ### Hypothesis Testing of Costa Rican Three-wattled Bellbird Loudness**Context:**Males of the Costa Rican three-wattled bellbird are considered the loudest birds globally. Their call, reaching an audience over half a mile away, is claimed to