A random sample of the number of unhealthy air days in 10 metropolitan regions, based on the AQI (Air Quality Index), is given below. Construct a 90% confidence interval for the true population mean number of unhealthy air days. Write a sentence to interpret the interval. (Round final values to 2 decimal places). 601294027389051340 This image contains a t-distribution critical values table (Table D) along with a diagram illustrating the t-distribution curve. Here’s a detailed breakdown:### Diagram Explanation:- **T-Distribution Curve**: - The diagram shows a bell-shaped t-distribution curve. - It highlights an area under the curve representing the upper-tail probability \( p \). - The critical value \( t^* \) is marked on the horizontal axis. This value separates the shaded area (representing probability \( p \)) from the rest of the curve. - The text explains that the table entry for \( p \) and \( C \) is the critical value \( t^* \) with probability \( p \) lying to its right and probability \( C \) lying between \(-t^*\) and \( t^* \).### Table D Explanation: t distribution critical values- **Columns**: - The columns are labeled with different upper-tail probabilities \( p \): .25, .20, .15, .10, .05, .025, .02, .01, .005, .0025, .001, .0005. - **Rows**: - The first column lists the degrees of freedom \( df \). - The table entries provide the critical values \( t^* \) corresponding to each degree of freedom and upper-tail probability.- **Bottom Row**: - Labeled as \( z^* \), providing the critical values for different confidence levels \( C \) ranging from 50% to 99.9%.This table and diagram are crucial tools for statistical analysis, helping to determine the critical value \( t^* \) for conducting hypothesis tests and constructing confidence intervals based on the t-distribution.

As Prof. N. G. Das said "Confidence interval is an interval such that the probability of the unknown…

Answered: A random sample of the number of…

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 number of unhealthy air days in 10 metropolitan regions, based on the AQI (Air Quality
Index), is given below. Construct a 90% confidence interval for the true population mean number of unhealthy
air days. Write a sentence to interpret the interval. (Round final values to 2 decimal places).

This image contains a t-distribution critical values table (Table D) along with a diagram illustrating the t-distribution curve. Here’s a detailed breakdown:

### Diagram Explanation:
- **T-Distribution Curve**:
- The diagram shows a bell-shaped t-distribution curve.
- It highlights an area under the curve representing the upper-tail probability \( p \).
- The critical value \( t^* \) is marked on the horizontal axis. This value separates the shaded area (representing probability \( p \)) from the rest of the curve.
- The text explains that the table entry for \( p \) and \( C \) is the critical value \( t^* \) with probability \( p \) lying to its right and probability \( C \) lying between \(-t^*\) and \( t^* \).

### Table D Explanation: t distribution critical values
- **Columns**:
- The columns are labeled with different upper-tail probabilities \( p \): .25, .20, .15, .10, .05, .025, .02, .01, .005, .0025, .001, .0005.

- **Rows**:
- The first column lists the degrees of freedom \( df \).
- The table entries provide the critical values \( t^* \) corresponding to each degree of freedom and upper-tail probability.

- **Bottom Row**:
- Labeled as \( z^* \), providing the critical values for different confidence levels \( C \) ranging from 50% to 99.9%.

This table and diagram are crucial tools for statistical analysis, helping to determine the critical value \( t^* \) for conducting hypothesis tests and constructing confidence intervals based on the t-distribution.

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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