1 In a study to determine the size of loan requests at a suburban bank, the mean in a random sample of 25 requests was $7500, with a standard deviation of $2000. Assuming that loan requests are normally distributed, estimate with 95% confidence the mean loan request. X = Size of loan request ($) State the data type and parameter of interest. Data type: Parameter of interest: What is the point estimator of this parameter and what is the sampling distribution of the standardised value of the point estimator. State and verify any required conditions. Point estimator: Standardised point estimator: Sampling distribution of the standardised point estimator: Is the required condition(s) satisfied? Why? Specify the formula for the 90% confidence interval estimator for the mean size of loan request. Calculate the 90% confidence interval of the mean size of loan request. Lower Limit = Upper Limit = 90% confidence interval of the mean loan request: Interpret the confidence interval obtained above with respect to the problem.

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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1 In a study to determine the size of loan requests at a suburban bank, the mean in a random sample of 25 requests was $7500, with a standard deviation of $2000. Assuming that loan requests are normally distributed, estimate with 95% confidence the mean loan request.

X = Size of loan request ($)

State the data type and parameter of interest.

Data type:

Parameter of interest:

What is the point estimator of this parameter and what is the sampling distribution of the standardised value of the point estimator. State and verify any required conditions.

Point estimator:

Standardised point estimator:

Sampling distribution of the standardised point estimator:

Is the required condition(s) satisfied? Why?

Specify the formula for the 90% confidence interval estimator for the mean size of loan request.

Calculate the 90% confidence interval of the mean size of loan request.

Lower Limit =

Upper Limit =

90% confidence interval of the mean loan request:

Interpret the confidence interval obtained above with respect to the problem.

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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