A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that a is $1.91. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.The 90% confidence interval is($____,$____) (Round to two decimal places as needed.)The 99% confidence interval is($____,$____) (Round to two decimal places as needed.) ### Confidence Interval Calculation for Stock Prices**Scenario:**A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the standard deviation ($\sigma$) is $1.91.**Stock Prices:**- 18.08- 16.45- 20.88- 15.65- 17.09- 15.64- 19.56- 16.84- 15.79- 20.42- 16.95- 19.31- 15.38- 18.69- 21.66- 17.14**Task:**Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.**Explanation:**- **90% Confidence Interval:** This interval gives the range within which you can be 90% confident that the true population mean lies. The width of this interval indicates the level of certainty about the mean. - **99% Confidence Interval (Not Shown):** While this is not depicted in the image, constructing a 99% confidence interval would provide a wider range than the 90% interval, reflecting increased certainty (but less precision) about the mean.**Interpretation:**The 90% confidence interval shown on the image suggests a range that estimates where the true mean of the stock prices lies, with a confidence level of 90%. By comparing the widths of the 90% and 99% confidence intervals, one would notice that a higher confidence level (99%) results in a wider interval.**Calculation Note:**To find the specific numerical interval, the appropriate statistical methods and software would complete the calculations based on the given data and standard deviation.This exercise demonstrates an important concept in statistics: the trade-off between the level of confidence and the precision of your estimate.

Answered: A random sample of the closing stock…

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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Question

A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that a is $1.91. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. The 90% confidence interval is($____,$____) (Round to two decimal places as needed.) The 99% confidence interval is($____,$____) (Round to two decimal places as needed.)

### Confidence Interval Calculation for Stock Prices

**Scenario:**
A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the standard deviation ($\sigma$) is $1.91.

**Stock Prices:**
- 18.08
- 16.45
- 20.88
- 15.65
- 17.09
- 15.64
- 19.56
- 16.84
- 15.79
- 20.42
- 16.95
- 19.31
- 15.38
- 18.69
- 21.66
- 17.14

**Task:**
Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

**Explanation:**

- **90% Confidence Interval:** This interval gives the range within which you can be 90% confident that the true population mean lies. The width of this interval indicates the level of certainty about the mean.

- **99% Confidence Interval (Not Shown):** While this is not depicted in the image, constructing a 99% confidence interval would provide a wider range than the 90% interval, reflecting increased certainty (but less precision) about the mean.

**Interpretation:**
The 90% confidence interval shown on the image suggests a range that estimates where the true mean of the stock prices lies, with a confidence level of 90%. By comparing the widths of the 90% and 99% confidence intervals, one would notice that a higher confidence level (99%) results in a wider interval.

**Calculation Note:**
To find the specific numerical interval, the appropriate statistical methods and software would complete the calculations based on the given data and standard deviation.

This exercise demonstrates an important concept in statistics: the trade-off between the level of confidence and the precision of your estimate.

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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