Answered: The 90% confidence interval is…

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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Section 6.1, please help with TI-84 commands if possible

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of 40 business days, the mean closing price of a certain stock was $124.93. Assume the population standard deviation is $11.04.

The 90% confidence interval is _________, _______________ (round to 2 decimal places)

The 95% confidence interval is _________, _______________(round to 2 decimal places)

Which interval is wider

The 90% confidence interval or 95% confidence interval

Interpret the results:

A. You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% interval and 95% confidence interval

B. You can be certain the closing price of the stock was within the 90% confidence interval for approximately 36 of the confidence interval for approximately 38 of the 40 days.

C. You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval and 95% interval.

D. You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% bounds of the 90% and 95% confidence intervals.

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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