A bank took a sample of 100 of its delinquent credit card accounts and found that the mean owed on these accounts was $2,130. It is known that the standard deviation for all delinquent credit card accounts at this bank is $578.(Hint: First write out the values for n, x¯, and σ)1. What is the margin of error for the sample mean at a 95% confidence level? Hint: Look at the notes given above to see how the margin of error is computed. 2. Will the margin of error increase/decrease if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the margin of error is computed and how the sample size n impacts its value. 3. Give a 95% confidence interval for the mean amount owed on all delinquent credit card accounts for this bank (i.e. population mean µ). Hint: Look at the notes given above to see how the confidence interval for the population mean is computed. 4. Will the confidence interval become wider or narrower if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the confidence interval is computed and how the sample size n impacts its lower and upper bounds and hence the width. 5. Will the confidence interval become wider or narrower if the sample size is still 100 but the confidence level is increased from 95% to 99%? Why? Hint: Look at the notes given above to see how the confidence interval is computed and how the multiplier depends on confidence level i.e. z∗ impacts its lower and upper bounds and hence the width. A population mean is the numerical average of a variable in the entire population of interest. One example would be the average amount spent odairy products by adult Americans in the previous year. The actual numerical value of a population mean would rarely be known.A sample mean is the numerical average of the data for a variable in a sample. One example would be the average amount spent on dairy productin the previous year by the respondents to a sample survey. The value of the sample mean might be used to estimate an unknown populationmean.The Standard Error of a sample Mean (often abbreviated S.E.M.) is the standard deviation of the sampling distribution of a sample mean. In arandom sample, it is estimated by (the sample standard deviation divided by the square root of the sample size).Chapter 5 discusses the likelihood of observing sample means in a specific range from a population with a known mean and standard deviation.ConcludeWhat does our knowledge ofthe parameter values tell usabout the population?ParametersInferenceWe want to infer what parametervalues are most consistent withthe sample statistic at hanPopulationSTATISTICALPARADIGMStatistical Summariesand PicturesProbabilityThe rules of probability tell usthe likelihood of different typesof samples that might arise froma particular population.SamplesDescribe and CompareData is collected from the samplesand, with sample data in hand, weattempt to create statisticalsummaries and pictures that give thesalient features of the data collected. Confidence Intervals for a population mean (n ≥) 30For large random samples, a confidence interval for a population mean is given bysample mean ±ME(sample mean) = sample mean ± z*SE(sample mean) = sample mean ±(z*vñ)where z* is a multiplier number that comes from the normal curve and determines the level of confidence.Multiplier Number (z*)3.02.58 (2.576)2.0 (more precisely 1.96)1.6451.2821.151.0Level of Confidence99.7%99%95%90%80%75%68%

as per policy i have calculated 3 subparts ,plz repost for remaining. A bank took a sample of 100 of…

Answered: What is the margin of error for the…

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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A bank took a sample of 100 of its delinquent credit card accounts and found that the mean owed on these accounts was $2,130. It is known that the standard deviation for all delinquent credit card accounts at this bank is $578.

(Hint: First write out the values for n, x¯, and σ)

1. What is the margin of error for the sample mean at a 95% confidence level? Hint: Look at the notes given above to see how the margin of error is computed.

2. Will the margin of error increase/decrease if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the margin of error is computed and how the sample size n impacts its value.

3. Give a 95% confidence interval for the mean amount owed on all delinquent credit card accounts for this bank (i.e. population mean µ). Hint: Look at the notes given above to see how the confidence interval for the population mean is computed.

4. Will the confidence interval become wider or narrower if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the confidence interval is computed and how the sample size n impacts its lower and upper bounds and hence the width.

5. Will the confidence interval become wider or narrower if the sample size is still 100 but the confidence level is increased from 95% to 99%? Why?

Hint: Look at the notes given above to see how the confidence interval is computed and how the multiplier depends on confidence level i.e. z∗ impacts its lower and upper bounds and hence the width.

A population mean is the numerical average of a variable in the entire population of interest. One example would be the average amount spent o
dairy products by adult Americans in the previous year. The actual numerical value of a population mean would rarely be known.
A sample mean is the numerical average of the data for a variable in a sample. One example would be the average amount spent on dairy product
in the previous year by the respondents to a sample survey. The value of the sample mean might be used to estimate an unknown population
mean.
The Standard Error of a sample Mean (often abbreviated S.E.M.) is the standard deviation of the sampling distribution of a sample mean. In a
random sample, it is estimated by (the sample standard deviation divided by the square root of the sample size).
Chapter 5 discusses the likelihood of observing sample means in a specific range from a population with a known mean and standard deviation.
Conclude
What does our knowledge of
the parameter values tell us
about the population?
Parameters
Inference
We want to infer what parameter
values are most consistent with
the sample statistic at han
Population
STATISTICAL
PARADIGM
Statistical Summaries
and Pictures
Probability
The rules of probability tell us
the likelihood of different types
of samples that might arise from
a particular population.
Samples
Describe and Compare
Data is collected from the samples
and, with sample data in hand, we
attempt to create statistical
summaries and pictures that give the
salient features of the data collected.

Confidence Intervals for a population mean (n ≥) 30
For large random samples, a confidence interval for a population mean is given by
sample mean ±ME(sample mean) = sample mean ± z*SE(sample mean) = sample mean ±(z*vñ)
where z* is a multiplier number that comes from the normal curve and determines the level of confidence.
Multiplier Number (z*)
3.0
2.58 (2.576)
2.0 (more precisely 1.96)
1.645
1.282
1.15
1.0
Level of Confidence
99.7%
99%
95%
90%
80%
75%
68%

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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