Question

The ozone dataset gives a sample of ozone measurements (in partial pressures) taken over the South Pole on September 18, 1997 at altitudes above 10km. (IF POSSIBLE INCLUDE R CODES FOR EACH QUESTION)

mPa: 1.828, 2.652, 3.307, 3.855, 4.021, 4.173, 4.316, 4.951, 4.787, 4.554, 4.333, 4.039, 4.48, 4.739, 4.791, 5.213, 5.75, 5.79, 5.656, 5.464, 5.092, 3.135, 2.754, 3.14, 5.213, 5.831, 5.736, 5.333, 4.797, 6.704, 6.493, 5.746, 6.31, 6.53, 6.63, 6.071, 5.706, 4.951, 4.392, 4.619, 5.029, 5.302, 5.151, 3.474, 3.285, 3.232, 3.4, 3.503, 3.649, 3.828, 4.235, 4.781, 5.096, 5.262, 5.411, 5.439, 5.08, 4.719, 4.519

1. Compute the five-number summary and sketch the boxplot. Identify any outliers.

2. Compute the mean and standard deviation of the sample.

3. Construct the probability plot of the data.

A hypothesis test could be used to compare the mean ozone level on September 18, 1997 to a specified baseline level.

4. Are the assumptions for an hypothesis test of the mean reasonably satisfied?

5. Test to see if the mean ozone amount on September 18 was below 5 mPa, at the 5% level of significance.

The following table gives data on the size of the Antarctic ozone hole (in millions of square kilometers), between 1979 and 1994.

Year	106 × km2
1979	2.23
1980	1.88
1981	1.70
1982	3.77
1983	6.24
1984	8.66
1985	12.57
1986	9.58
1987	18.18
1988	8.75
1989	17.75
1990	17.86
1991	18.13
1992	21.28
1993	22.81
1994	22.82

6. Construct a line graph of the data in the table. Note any trends that you see.

7. Does it make sense to apply inferential methods (of the type we have studied) to the mean size of the ozone hole over time? Explain.

In addition to plotting the ozone concentration versus time, create a linear regression model for it and interpret the slope and comment on how well the model fits the data using the coefficient of variation.

Answer 1

R version 3.6.0 (2019-04-26) -- "planting of a Tree" Copyright (c) 2019 The R Foundation for statistical computing platform: x86_64-W64-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type license()' or 'licence()' for distribution details. Ris a collaborative project with many contributors. Type 'contributors ('for more information and 'citation on how to cite R or R packages in publications. Type 'demo ' for some demos, 'help ' for on-line help, or "help.start()' for an HTML browser interface to help. Type '90' to quit R. >x<- c(1.828, 2.652, 3. 307, 3.855, 4.021, 4.173, 4.316, 4.951, 4.787, 4.554, 4.333, 4.039, 4.48, 4.739, 4.791, 5.213, 5.75, 5.79, 5.656, 5.464, 5.092, 3.135, 2.754, 3.14, 5.213, 5.831, 5.736, 5.333, 4.797, 6.704, 6.493, 5.746, 6.31, 6.53, 6.63, 6.07 1, 5.706, 4.951, 4.392, 4.619, 5.029, 5. 302, 5.151, 3.474, 3.285, 3.232, 3.4, 3.503, 3.649, 3.828, 4.235, 4.781, 5.096, 5.262, 5.411, 5.439, 5.08, 4.719, 4.519) [1] 1.828 2.652 3.307 3.855 4.021 4.173 4.316 4.951 4.787 4.554 4. 333 [12] 4.039 4.480 4.739 4.791 5.213 5.750 5.790 5.656 5.464 5.092 3.135 [23] 2.754 3.140 5.213 5.831 5.736 5.333 4.797 6.704 6.493 5.746 6. 310 [34] 6.530 6.630 6.071 5.706 4.951 4.392 4.619 5.029 5. 302 5.151 3.474 [45] 3.285 3.232 3.400 3.503 3.649 3.828 4.235 4.781 5.096 5.262 5.411 [56] 5.439 5.080 4.719 4. 519 > Summary (x, quantile.type = 7) Min. 1st Qu. Median Mean 3rd Qu. Max. 1.828 4.030 4.7914.717 5.425 6.704 > sd(x, na.rm = FALSE) [1] 1.073852 > count(x) Error in count(x) : could not find function "count" > rnorm(59, m= 4.717,sd =1.074) [1] 4.0823532 2.7131336 5.7415661 5.7518495 5.8572272 0.7242475 [7] 5. 2414942 3.7185571 5.6892819 6.0507527 4.7717975 5.4940158 [13] 4.6965253 4.091 8414 4.2333 304 5.57 31834 4.2880415 5.9915249 [19] 3.9808025 3.8736525 5.6722 371 5. 5443931 2.6422255 4. 2029487 [25] 5.0224960 5.9311162 4.2381158 4.3783999 4.2803722 3.8568201 [31] 5.3635480 3.8201112 3.0113343 4.5126921 4.4283982 3.8207452 [37] 4.6885261 5.4016233 4.4358929 6.3473369 5.2792149 4.4238211 [43] 6. 2705670 5.6955937 4.5450994 2. 3097617 4.4387719 3.9282295 [49] 3. 6447682 4.5838512 4.6914886 4.2451338 5.1064606 4.7770325 [55] 3.4047801 4.2577806 3. 9651733 4.8372890 4.7487108 > boxplot(x)