Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Solution Summary: The author explains how to perform a z-test to determine whether the population proportion is different from 10.1 or not.
Self-Employment According to the Bureau of Labor Statistics,
10.1
%
of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed.
a. Test the hypothesis that the proportion of self-employed workers in this area is different from
10.1
%
.
Use a
0.05
significance level.
b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a
95
%
confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
To: [Boss's Name]
From: Nathaniel D Sain
Date: 4/5/2025
Subject: Decision Analysis for Business Scenario
Introduction to the Business Scenario
Our delivery services business has been experiencing steady growth, leading to an
increased demand for faster and more efficient deliveries. To meet this demand,
we must decide on the best strategy to expand our fleet. The three possible
alternatives under consideration are purchasing new delivery vehicles, leasing
vehicles, or partnering with third-party drivers. The decision must account for
various external factors, including fuel price fluctuations, demand stability, and
competition growth, which we categorize as the states of nature. Each alternative
presents unique advantages and challenges, and our goal is to select the most
viable option using a structured decision-making approach.
Alternatives and States of Nature
The three alternatives for fleet expansion were chosen based on their cost
implications, operational efficiency, and…
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