A 2008 survey of low- and middle-income households conducted by Demos, a liberal public group, showed that consumers aged 65 years and older had an average credit card debt of $11,535 and consumers in the 50- to 64-year age group had an average credit card debt of $10642 at the time of the survey (USA TODAY, July 28, 2009). Suppose that these averages were based on random samples of 1000 and 1200 people for the two groups, respectively. Further assume that the population standard deviations for the two groups were $2200 and $2500, respectively. Let u1 and µ2 be the respective population means for the two groups, people aged 65 years and older and people in the 50- to 64-year age group. (a) What is the point estimate of u1 - µ2? (b) Construct 98% confidence interval for µ1 – µ2 and interpret the results. (c) What is the margin of error?

A 2008 survey of low- and middle-income households conducted by Demos, a liberal public group, showed that consumers aged 65 years and older had an average credit card debt of $11,535 and consumers in the 50- to 64-year age group had an average credit card debt of $10642 at the time of the survey (USA TODAY, July 28, 2009). Suppose that these averages were based on random samples of 1000 and 1200 people for the two groups, respectively. Further assume that the population standard deviations for the two groups were $2200 and $2500, respectively. Let u1 and µ2 be the respective population means for the two groups, people aged 65 years and older and people in the 50- to 64-year age group. (a) What is the point estimate of u1 - µ2? (b) Construct 98% confidence interval for µ1 – µ2 and interpret the results. (c) What is the margin of error?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

A 2008 survey of low- and middle-income households conducted by Demos, a liberal public group,
showed that consumers aged 65 years and older had an average credit card debt of $11,535 and
consumers in the 50- to 64-year age group had an average credit card debt of $10642 at the time of the
survey (USA TODAY, July 28, 2009). Suppose that these averages were based on random samples of
1000 and 1200 people for the two groups, respectively. Further assume that the population standard
deviations for the two groups were $2200 and $2500, respectively. Let µ1 and µ2 be the respective
population means for the two groups, people aged 65 years and older and people in the 50- to 64-year
age group.
(a) What is the point estimate of u1 - µ2?
(b) Construct 98% confidence interval for u1 - µ2 and interpret the results.
(c) What is the margin of error?
(d) Conduct the appropriate two-tailed test at 5% level of significance.

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