Question

GMU officials are trying to determine if they are using the
correct number of campus shuttles for the number of individuals who
use them. If the proportion of individuals associated with GMU
(including faculty, staff, and students) who use the shuttles is
significantly different from 0.28, the officials believe they will
have to either remove or add a shuttle to the fleet. In a random
sample of 444 people taken from the population of all individuals
associated with GMU (including faculty, staff, and students) it was
discovered that 123 of these individuals use the shuttle.

a) Check the three conditions of the Central Limit Theorem that
allow you to use the oneproportion confidence interval using one
complete sentence for each condition. Show work for the numerical
calculation.

b) Construct a 99% confidence interval to estimate the population
proportion of these individuals who use the shuttle system.
Calculate this “by hand” using the formula and showing your work
(please type your work, no images accepted here). Round your
confidence limits to four decimals.

c) Verify your result in part (b) using Stat Proportions Stats
One Sample With Summary. Copy and paste your StatCrunch result in
your document as well.

d) Using = 0.01, is there sufficient evidence to conclude that
the proportion of the individuals who use GMU shuttles is different
from 0.28? Conduct a full hypothesis test by following the steps
below. Enter an answer for each of these steps in your
document.

i. Define the population parameter in one sentence.

ii. State the null and alternative hypotheses using correct notation.

iii. State the significance level for this problem.

iv. Calculate the test statistic “by-hand.” Show the work
necessary to obtain the value by typing your work and provide the
resulting test statistic. Do not round

during the calculation. Then, round the test statistic to two
decimal places after you complete the calculation.

v. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value.

vi. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this).

vii. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

viii. Use StatCrunch (Stat Proportion Stats One Sample
with Summary) to verify your test statistic and p-value. Copy and
paste this box into your document.

e) Explain the connection between the confidence interval and the
hypothesis test in this problem (discuss this in relation to the
decision made from your hypothesis test and connect it to the
confidence interval you constructed in part (b)). Answer this
question in one to two sentences.

Answer #1

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For this project, you will make decisions about how two
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Sample mean () Body Mass Index (BMI)
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Sample standard deviation (s) of Body Mass Index (BMI)
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Sample size
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It's flu season on campus. A study reported that 10% of students
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Suppose 200 students and 200 faculty & staff responded to the
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In the 2000 football season, 247 plays were reviewed by
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49
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1) You want to determine if the proportion of people who will
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A researcher is trying to determine whether there is a
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