General Instructions I Write the answers for each part of each exercise in a word document I Upload your Lab Assignment 1 word document on Angel I Any figures you are required to do can either be inserted in the word document or attached in the email In the latter case it should be made clear which exercise each figure corresponds to Lab Assignment 1 Exercise 1 Import nto the R object cs data on 28 day compressive strength measurements of concrete cylinders using water cement ratio 0 4 using the command cs read table http sites stat psu edu mga 401 Data Concr Strength 1s Data txt header T Then use the commands attach cs sum Str 44 length Str sum Str 47 length Str to obtain the proportion of measurements that are less than or equal to 44 and greater than or equal to 47 What do these sample proportions estimate Lab Assignment 1 Exercise 2 a Using R commands find the mean the variance and standard deviation of the statistical population corresponding to the number of scratches of 500 tin plates where 190 have 0 scratches 160 have 1 scratch and 150 have 2 scratches In addition to reporting the results you obtained give the R commands you used to set up the statistical population and to do the calculations Note R as well as your calculator always compute the sample variance Multiply it by 499 500 to get the population variance b Use R to get a simple random sample of 100 from this statistical population and to compute the sample proportions for each of the three categories the mean variance and standard deviation of the sample you obtained In addition to reporting the results you obtained give the R commands you used to obtain the sample and to do the calculations Lab Assignment 1 Exercise 3 a Use the commands attach faithful hist waiting stem waiting to do a basic histogram of the Old Faithful data on waiting times before eruptions and the corresponding stem and leaf plot Is the shape of the stem and leaf plot similar to that of the histogram b Redo the histogram but this time add color to the bars superimpose a colored smooth histogram and add a histogram title Lab Assignment 1 Exercise 4 The data in http sites stat psu edu mga 401 Data Temp Long Lat txt source Peixoto J L 1990 A property of well formulated polynomial regression models American Statistician 44 26 30 give the average over the years 1931 to 1960 daily minimum January temperature in degrees Fahrenheit with the latitude and longitude of 56 U S cities a Do a scatterplot matrix of the data Does longitude or latitude appear to be the better predictor of a citys temperature Explain in terms of this plot b Do a 3d scatterplot of the data Does longitude or latitude appear to be the better predictor of a citys temperature Explain in terms of this plot Lab Assignment 1 Exercise 5 Read the data on the average stopping times on a level dry stretch of highway free from loose material of cars and trucks at various speeds into the data frame bd by bd read table http sites stat psu edu mga 401 Data SpeedStopCarTruck txt header T Do a scatterplot of the data using colors to differentiate between cars and trucks and dd a legend to the plot Lab Assignment 1