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##### Statistics project

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solution

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Question;Statistics project;This project will involve the gathering of samples and the;use of both descriptive and inferential statistics. It will be due by December;17th.;All work must be shown and the write up must;be typed (mathematical formulations may be hand written). You may use any;software with statistical applications (Excel, StatCrunch, Minitab, etc.);calculator or any other statistical tool for your analysis work (there are some;online tools that can calculate confidence intervals and hypothesis tests). You;may also use the textbook and any other written resource to aid you in your;work (website, etc.). The work on this project must be your own. Seeking assistance from anyone else (Tutor;Classmate, etc.) is strictly forbidden (you are on your honor).I;will be available to answer any questions that you may have for this project;for clarity purposes.;Project Concept;This project will focus on analyzing weather data for two;cities in upstate New York (Binghamton and Syracuse). The data is located on;the NOAA website. The project will be in three parts;Part 1: Perform a descriptive and numerical analysis;of a sample of average daily temperatures for the city of Syracuse, NY.;Part 2: Create confidence intervals to estimate the average monthly;precipitation for both Syracuse and Binghamton, NY.;Part 3: Using a two-sample dependent (matched pairs) design, determine;if there exists a difference in average winter monthly snowfall.;Data Needed for the Project;The NOAA website contains the data needed to perform the;analysis. There will be instructions on how to get to the website and navigate;to the locations of where the data can be found. For all three parts please;restrict yourself within the time period from January 1965 to December 2012.;Part 1: Descriptive and Numerical Analysis;for Syracuse, NY (1965 to 2012);For this part of the project you need to gather the daily average temperature for 50 different days from January;1965 to December 2012 for Syracuse, NY. At the end of this project document I;will provide some details of what can be used to gather this sample properly.;Part 2: Confidence Interval Estimates for Monthly;Precipitation for Binghamton and Syracuse, NY (1965 to 2012);For this part of the project you need to gather the total;monthly precipitation for 30;different months from January 1965 to December 2012 for Binghamton and;Syracuse, NY. You must gather a different simple random sample (SRS) of 30;months for each city (one set of 30 months for Binghamton and a separate set of;30 months for Syracuse). At the end of this project document I will provide;some details of what can be used to gather this sample properly. I have created;a chart (called Part 2 Data Sheet) that will help you organize this data.;Part 3: Two-Sample Dependent (Matched Pairs) Design for;Winter Month Snowfall (1965 to 2012);For the last part of the project you need to gather a;matched pair design sample of monthly total snowfall totals for 30 different ?winter? months;from January 1965 to December 2012 for Binghamton and Syracuse. Winter months;will be defined as December, January, February and March. This sample differs;from the other parts of the project in that you only need to obtain oneSRS of 30 different winter;months. Once that sample is created then you need to get the monthly snowfall;totals for both Binghamton and Syracuse for that month (i.e. if one of your;months is February 1992 then you need to gather the snowfall totals for both;Binghamton and Syracuse for February 1992). I have created a chart (called Part;3 Data Sheet) that will help you organize this data.;Statistical Analysis;Part 1: Descriptive and Numerical;Analysis;Using the sample of average daily temperatures gathered for;Syracuse, NY please conduct the following descriptive and numerical analysis.;Stem-and-Leaf PlotFrequency Table using;between 6 and 10 classes (your choice)Frequency Histogram based;on the frequency table you createdFive Number Summary and;Boxplot (including fences)Mean, Median, and ModeStandard Deviation;*note: for the purposes of calculating mean and standard;deviation you do not need to calculate it by hand (you may use the statistical;features of your calculator or computer instead);Part 2: Confidence Interval Estimator;Using the Part 2 data gathered please create a 95%;confidence interval estimator for the population average monthly precipitation;for Binghamton and Syracuse, NY. In other words, you will create two different;95% confidence intervals, one for Binghamton and another for Syracuse.;Part 3: Two-sample Dependent (Matched Pairs) Design Hypothesis Test;Using the Part 3 data gathered please run a dependent;hypothesis test for the population difference of monthly average snowfall at;the 5% level of significance. Please be sure to show all four steps of the;hypothesis test (you may use the p value approach for this if you wish). Note;you do not need to show me the work for the mean and standard deviation;calculations since you can use the statistical functions of your calculator for;them.;Project Summary;For the final part of the project I would like you to answer;the following questions below.;a) Using;the Descriptive Analysis from part 1, does it appear that the population of average;daily temperatures for Syracuse, NY is normally distributed? Why or why not?;b) Using;the confidence intervals from part 2, is it possible that the population means;of monthly precipitation for Binghamton and Syracuse, NY are the same? Why or;why not?;c) Using;the dependent hypothesis test from part 3, what were you able to conclude about;the difference of monthly snowfall between Binghamton and Syracuse (i.e. did;one of the cities appear to have a higher average monthly snowfall total?);d) The;sample size for parts 2 and 3 of the analysis were set at 30 (hint: it had to;be at least 30). Why is this important?;e) In;the past students have tried to use the random date generator from random.org;to gather their part 2 data by ignoring the day and using just the month and;year (i.e. if they got a date of 3/20/1977, they would throw out the 20 and use;just 3/1977 as their random month). Does this process actually result in a true;simple random sample? Why or why not?;Write Up Details;When putting the project together for submission please make;sure the materials are in the following order;Cover Page (with your name;and date)The raw data you gathered;(for parts 1,2, and 3 of the project)Part 1 AnalysisPart 2 AnalysisPart 3 AnalysisProject Summary Questions;Please be sure to type all that you can for this project. If;hand calculations need to be shown please be sure they are clear and legible.;Random;Sample Resources;For part 1 of the project;I highly recommend using the calendar date generator found on the;random.org website. The address is;http://www.random.org/calendar-dates/;Be sure to include all days of the week when using this;feature (it defaults to just weekdays).;For parts 2 and 3 you can;use random.org to generate lists of integers. The address is;http://www.random.org/integers/;For the part 2 months, generate two separate lists of at;least 30 values. One that uses digits 1-12 (for the months) and the other that;uses digits 1965-2011 (for the years). You can then merge them together for;your month/year combo.;For the part 3 months, use the same process as the part 2;process except use 0-3 for your winter months..;0 = December, 1 =;January, 2 = February, 3 = March;I highly recommend gathering more than 30 random months for;parts 2 and 3. So if you get a repeat month/year you can ignore it and move to;the next month/year for your sample.;Part 1 Data Sheet;Number;Date;Average Temp;Number;Date;Average Temp;1;31;2;32;3;33;4;34;5;35;6;36;7;37;8;38;9;39;10;40;11;41;12;42;13;43;14;44;15;45;16;46;17;47;18;48;19;49;20;50;21;22;23;24;25;26;27;28;29;30;Part 2 Data Sheet;Binghamton;Syracuse;Number;Month;Total;Precipitation;Number;Month;Total;Precipitation;1;1;2;2;3;3;4;4;5;5;6;6;7;7;8;8;9;9;10;10;11;11;12;12;13;13;14;14;15;15;16;16;17;17;18;18;19;19;20;20;21;21;22;22;23;23;24;24;25;25;26;26;27;27;28;28;29;29;30;30;Part 3 Data Sheet;Number;Month;Total Monthly;Snowfall for Syracuse;Total Monthly;Snowfall for Binghamton;Difference;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;Finding Data on the;NOAA Website (Part 1);To find the data required for the project;Go;to website location: www.erh.noaa.gov/bgm/In;the left panel under Climate choose Local.Above;Observed Weather Reports choose Local Data/Records.Under;Climate Data choose Local Records and Averages.Above;Local Climate Information choose your city (Binghamton, Scranton or;Syracuse)Use;Past Preliminary Climatology Data (CF6). There will be two drop;tabs (one for month and one for year).. Select your month/year and then;choose Get Data;This should get you to the web page with weather;information. Please read Part 2 to learn how to find the data needed on the;page.;There are appears to be two different formats for the;weather data to be displayed when you look up a month;Example of FORMAT 1.;This is the standard format that most months may be;presented as. The example below is of March 1994 for Binghamton, NY (BGM).;DAY = Day of the month;For Part 1 of the project you will be using the AVG Column;(for the daily Average temperature).;For Part 2 of the project (monthly total precipitation) you;will look at the bottom of the PCPN column to get the monthly precipitation;(cross reference with the Total row). In this example the total monthly;precipitation is 5.06 inches.;For Part 3 of the project (monthly total snowfall) you will;look at the bottom of the SNOW column to get the monthly snowfall (cross;reference with the Total row). In this example the total monthly snowfall is;27.8 inches.;Example of FORMAT 2;Format 2 looks much like format 1. When you need to find;information that is used for Parts 1 they exist in the same column just like;format 1. Finding total monthly precipitation and snowfall (for Parts 2 and 3);becomes a little more involved in format 2. The best way to find it is to move;down the page a little and look for the following (this is an example of March;1999 for Binghamton);Note that I circled where you can find the Total Monthly;Precipitation and Snowfall (2.57 inches of precipitation and 33.8 inches of;snow for this month).;Looking over the website it looks like much of the older;information is in Format 1 and the newer information is in Format 2. If you;have any difficulty finding information please do not hesitate to ask.

Paper#61190 | Written in 18-Jul-2015

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