Consistency of the Weather Nicole Baratelle, Cara Barskey, Youjin Kwon

Topic To determine the accuracy of the weather Used the normal and actual temperature for specific days to see if difference in mean temperature Analyzed mean difference Information from the National Oceanic & Atmospheric Administration (NOAA) –National Weather Service

Procedure Mean Difference 1-Sample T- Test/ Confidence Interval –SRS of 50 Days in 2008 (numbered, software) –Found average temperature on each day (avg. observed & avg. normal) –Mean Difference ( observed- normal ) –Analyzed accuracy of weather by performing 1-Sample T-test and Confidence Interval for mean difference

Procedure (cont.) Mean Difference 2-Sample T- Test/ Confidence Interval –Two SRS’s  Summer Days (May-Oct.) & Winter Days (Nov.-April) –For each day, found observed and normal avg. temperature –Mean Difference ( observed- normal ) for each sample –Compared Accuracy of Summer and Winter months using 2-sample T-test for mean difference

Monthly weather predictions made in Farmers’ Almanac since 1818 with 80%-85% accuracy –Predictions made 2yrs in advance NOAA’s National Weather Service predicting weather since 1870 –Weekly weather predictions –Able to calculate daily “normal” –Daily Almanac gives temperature, precipitation, snow depth and the normals –Use Doppler Weather Radar to predict weather patterns Background

Data Yearly Average Temperatures

Data Winter Average Temperatures

Data Summer Average Temperatures

Exploratory Analysis

Yearly Average Temperatures

Conclusion Statistical summaries are similar but not the same Slight difference between the expected and normal temperatures

Conclusion Winter and summer expected graphs are both higher temperatures as compared to the observed graphs Therefore, both winter and summer expected over predicted No difference

Inferential Analysis

Assumptions 1.SRS yes  2.Normal population 50 or Mean Difference 1-Sample T-Test 

Mean Difference 1-Sample T-Test (cont.)

Conclusion: We reject in favor of because the P-value of <. We have sufficient evidence that the absolute value of differences between observed and expected temperatures is greater than zero. **Predicted and observed temperatures are different; therefore NOAA did not do great job predicting the temperatures in 2008.** Mean Difference 1-Sample T-Test (cont.)

Mean Difference 1-Sample Confidence Interval We are 95% confident that the absolute value of mean differences between observed and expected temperatures is between and °F; Zero is not in the interval so there is a significant difference between observed and predicted temperatures.

Mean Difference 2-Sample T-Test Assumptions 1. 2 independent SRS yes  2. 2 Normal populations or 40 

Mean Difference 2-Sample T-Test (cont.) Summer: May to October Winter: November to April

Conclusion: We fail to reject because the p- value of >. We have sufficient evidence that the mean difference between observed and predicted temperatures in the summer is equal to the mean difference between observed and predicted temperatures in the winter. **Incorrect predictions in summer months are equal to the incorrect predictions in winter months.** Mean Difference 2-Sample T-Test (cont.)

Mean Difference 2-Sample Confidence Interval We are 95% confident that the difference between the mean difference between observed and predicted temperatures in the summer and the mean difference between observed and predicted temperatures in the winter is between and °F. We conclude that the mean difference between observed and predicted temperatures in the summer is equal to the mean difference between observed and predicted temperatures in the winter since the interval contains 0, which makes two mean differences equal to each other.

Yearly Average Temperatures –Thought it would be off –Weather is never perfect –Climate changing Summer vs. Winter –Surprised that they are same mean difference –Winter temperatures seems to be more changing Personal Opinions/Conclusions

Use this to know how much you can trust the weather forecast Relation to global warming –See if there is a pattern of temperatures being warmer/cooler than normal Application to population

Used the average daily temperature –If outstanding high or low, avg. thrown off Used data collected from a internet site –Legitimate site but can never be certain Bias/Error

Activity

Date (2008)Class Predictions 1/6 7/8 5/4 9/10 10/11 1/22 7/24 4/9 12/1 7/16 3/29 3/20 5/6 11/10 4/3 6/7 6/20 5/23 1/15 8/9