need iv-vi please

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Submitted this once and they could only do i-iii, so I only need iv-vi please.

a) Males of the Costa Rican three-wattled bellbird are the loudest birds in the
world. Their bell-like mating song can be heard from over half a mile away by
humans. Juanita, your Costa Rican friend, saw a report online claiming that these
birds can be as loud as 100 dB (decibels). To put it in perspective, a live rock
concert makes around 100 dB of sound. While these birds can be quite loud, a
hundred decibels seems like an exaggeration. Skeptical, Juanita decides to
conduct a hypothesis test to decide whether the internet report can be trusted
based on a random sample of 9 adult male three-wattled bellbirds.
- Assume that the loudness of bellbird songs are approximately normally
distributed with mean u (in dB) and variance 02 (in dB2) - both unknown
(i)
O Ho:p=100, HA:ps100.
O Ho:p0100, HA:p<100.
O Ho:p=100, HA:p0100.
O Ho:p=100, HA:p<100.
O Ho:us100, HA:p>100.
(ii) The average loudness and variance for Juanita's sampled birds were
computed to be 94.619 dB and 49.0001 dB2 respectively. Conduct an appropriate
test to choose between the hypotheses you identified in (i), and report the
p-value, and your decision (accept or reject Ho) at a 2% level of significance (that
is, a = 0.02).
(iii) Construct a 95% confidence interval for p, and interpret it.
(iv) How large would the sample size need to be so that the margin of error for
your 95% confidence interval is at most 5?
(v) Unfortunately, Juanita has not taken statistics in college, and treats her
sample variance as the population variance, and carries out a test accordingly.
Find out what her p-value is, and whether she accepted or rejected Ho at the
same level of significance as in part (ii) above.
(vi) Do you think what test Juanita or you carry out would matter if the number of
birds chosen for this study was larger, say around 50? Why?
Transcribed Image Text:a) Males of the Costa Rican three-wattled bellbird are the loudest birds in the world. Their bell-like mating song can be heard from over half a mile away by humans. Juanita, your Costa Rican friend, saw a report online claiming that these birds can be as loud as 100 dB (decibels). To put it in perspective, a live rock concert makes around 100 dB of sound. While these birds can be quite loud, a hundred decibels seems like an exaggeration. Skeptical, Juanita decides to conduct a hypothesis test to decide whether the internet report can be trusted based on a random sample of 9 adult male three-wattled bellbirds. - Assume that the loudness of bellbird songs are approximately normally distributed with mean u (in dB) and variance 02 (in dB2) - both unknown (i) O Ho:p=100, HA:ps100. O Ho:p0100, HA:p<100. O Ho:p=100, HA:p0100. O Ho:p=100, HA:p<100. O Ho:us100, HA:p>100. (ii) The average loudness and variance for Juanita's sampled birds were computed to be 94.619 dB and 49.0001 dB2 respectively. Conduct an appropriate test to choose between the hypotheses you identified in (i), and report the p-value, and your decision (accept or reject Ho) at a 2% level of significance (that is, a = 0.02). (iii) Construct a 95% confidence interval for p, and interpret it. (iv) How large would the sample size need to be so that the margin of error for your 95% confidence interval is at most 5? (v) Unfortunately, Juanita has not taken statistics in college, and treats her sample variance as the population variance, and carries out a test accordingly. Find out what her p-value is, and whether she accepted or rejected Ho at the same level of significance as in part (ii) above. (vi) Do you think what test Juanita or you carry out would matter if the number of birds chosen for this study was larger, say around 50? Why?
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