Please write it step by step with no software for computing the problems ## Analysis of Temperature Changes from 1968 to 2008### IntroductionIs there strong evidence of global warming? Let’s consider a small-scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. We are interested in determining whether these data provide strong evidence of temperature warming in the continental US.### Questions for Analysis(a) **Independence of Observations** - Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain.(b) **Hypothesis Formation** - Write hypotheses for this research in symbols and in words.(c) **Conditions for Testing** - Check the conditions required to complete this test.(d) **Statistical Analysis** - Calculate the test statistic and find the p-value.(e) **Contextual Conclusion** - What do you conclude? Interpret your conclusion in context.(f) **Confidence Interval Calculation** - Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. Interpret this interval in context.(g) **Evaluating Evidence** - Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US? Explain.### Diagram ExplanationThere are no graphs or diagrams included in this content. However, you may consider creating a visual representation of the temperature differences, distribution of values, or a graph illustrating the confidence interval to enhance understanding.This analysis aims to provide a foundational understanding of statistical methods applied to real-world climate data and how such evidence can be interpreted within the context of global warming.

According to our guidelines we are allowed to answer three sub-parts (a) Since the temperatures are…

(a) Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain. (b) Write hypotheses for this research in symbols and in words. (c) Check the conditions required to complete this test.

(a) Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain. (b) Write hypotheses for this research in symbols and in words. (c) Check the conditions required to complete this test.

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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Please write it step by step with no software for computing the problems

## Analysis of Temperature Changes from 1968 to 2008

### Introduction

Is there strong evidence of global warming? Let’s consider a small-scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. We are interested in determining whether these data provide strong evidence of temperature warming in the continental US.

### Questions for Analysis

(a) **Independence of Observations**
- Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain.

(b) **Hypothesis Formation**
- Write hypotheses for this research in symbols and in words.

(c) **Conditions for Testing**
- Check the conditions required to complete this test.

(d) **Statistical Analysis**
- Calculate the test statistic and find the p-value.

(e) **Contextual Conclusion**
- What do you conclude? Interpret your conclusion in context.

(f) **Confidence Interval Calculation**
- Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. Interpret this interval in context.

(g) **Evaluating Evidence**
- Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US? Explain.

### Diagram Explanation

There are no graphs or diagrams included in this content. However, you may consider creating a visual representation of the temperature differences, distribution of values, or a graph illustrating the confidence interval to enhance understanding.

This analysis aims to provide a foundational understanding of statistical methods applied to real-world climate data and how such evidence can be interpreted within the context of global warming.

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