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source("http://www.openintro.org/stat/data/arbuthnot.R")
dim(arbuthnot)
## [1] 82  3
names(arbuthnot)
## [1] "year"  "boys"  "girls"

Excercise 1:

What command would you use to extract just the counts of girls baptized? Try it!

arbuthnot$girls
##  [1] 4683 4457 4102 4590 4839 4820 4928 4605 4457 4952 4784 5332 5200 4910
## [15] 4617 3997 3919 3395 3536 3181 2746 2722 2840 2908 2959 3179 3349 3382
## [29] 3289 3013 2781 3247 4107 4803 4881 5681 4858 4319 5322 5560 5829 5719
## [43] 6061 6120 5822 5738 5717 5847 6203 6033 6041 6299 6533 6744 7158 7127
## [57] 7246 7119 7214 7101 7167 7302 7392 7316 7483 6647 6713 7229 7767 7626
## [71] 7452 7061 7514 7656 7683 5738 7779 7417 7687 7623 7380 7288
plot(x = arbuthnot$year, y = arbuthnot$girls)

plot(x = arbuthnot$year, y = arbuthnot$girls, type = "l")

Excercise 2:

Is there an apparent trend in the number of girls baptized over the years? How would you describe it?

Answer: The number girls baptized started declining after 1640 and dropped significantly till 1660. From 1660 onwards the number continued to increase over the next 40 years. It went from below 3000 to around 7000 girls baptized per year.

plot(arbuthnot$year, arbuthnot$boys + arbuthnot$girls, type = "l")

arbuthnot$boys / (arbuthnot$boys + arbuthnot$girls)
##  [1] 0.5270175 0.5215244 0.5187705 0.5210768 0.5159548 0.5109082 0.5088698
##  [8] 0.5163831 0.5134279 0.5197362 0.5286700 0.5085714 0.5126523 0.5265188
## [15] 0.5093518 0.5067868 0.5080341 0.5260366 0.5177305 0.5139059 0.5285837
## [22] 0.5149679 0.5322023 0.5254569 0.5192526 0.5197885 0.5218447 0.5202837
## [29] 0.5080030 0.5116694 0.5357262 0.5342132 0.5361942 0.5206108 0.5257482
## [36] 0.5153557 0.5128359 0.5199511 0.5134394 0.5220493 0.5274422 0.5232975
## [43] 0.5155076 0.5128552 0.5105507 0.5158214 0.5144798 0.5284297 0.5087122
## [50] 0.5212285 0.5083822 0.5096910 0.5108199 0.5060426 0.5142178 0.5152360
## [57] 0.5080788 0.5155165 0.5174905 0.5132301 0.5147925 0.5199527 0.5089677
## [64] 0.5095857 0.5063659 0.5123973 0.5196766 0.5135590 0.5093183 0.5249190
## [71] 0.5149385 0.5176583 0.5188268 0.5119526 0.5026541 0.5158214 0.5181790
## [78] 0.5174052 0.5215362 0.5194175 0.5151117 0.5117899

Excercise 3:

Now, make a plot of the proportion of boys over time. What do you see?

plot(arbuthnot$year, arbuthnot$boys / (arbuthnot$boys + arbuthnot$girls), type = "l")

plot(x = arbuthnot$year, y = arbuthnot$boys, type = "l")

Answer: The ratio of boys being baptized is consistently higher between the range of 50 to 53%

library('DATA606')
## 
## Welcome to CUNY DATA606 Statistics and Probability for Data Analytics 
## This package is designed to support this course. The text book used 
## is OpenIntro Statistics, 3rd Edition. You can read this by typing 
## vignette('os3') or visit www.OpenIntro.org. 
##  
## The getLabs() function will return a list of the labs available. 
##  
## The demo(package='DATA606') will list the demos that are available.
## 
## Attaching package: 'DATA606'
## The following object is masked from 'package:utils':
## 
##     demo
vignette(package='DATA606') # Lists vignettes in the DATA606 package
## no vignettes found
vignette('os3')             # Loads a PDF of the OpenIntro Statistics book
## Warning: vignette 'os3' not found
data(package='DATA606')     # Lists data available in the package
getLabs()                   # Returns a list of the available labs
##  [1] "Lab0"  "Lab1"  "Lab2"  "Lab3"  "Lab4a" "Lab4b" "Lab5"  "Lab6" 
##  [9] "Lab7"  "Lab8"
#viewLab('Lab0')             # Opens Lab0 in the default web browser
#startLab('Lab0')            # Starts Lab0 (copies to getwd()), opens the Rmd file
shiny_demo()                # Lists available Shiny apps
##    package              app
## 1  DATA606   BayesBilliards
## 2  DATA606  BayesPopulation
## 3  DATA606         CLT_mean
## 4  DATA606         CLT_prop
## 5  DATA606 correlation_game
## 6  DATA606        dist_calc
## 7  DATA606       DualScales
## 8  DATA606          gambler
## 9  DATA606          lottery
## 10 DATA606         slr_diag
source("http://www.openintro.org/stat/data/present.R")

1:What years are included in this data set? What are the dimensions of the data frame and what are the variable or column names?

Answer: The years range from 1940 to 2002, Dimensions and column names are below

dim(present)
## [1] 63  3
names(present)
## [1] "year"  "boys"  "girls"
plot(x = present$year, y = present$girls, type = "l")

plot(x = arbuthnot$year, y = arbuthnot$girls, type = "l")

max(present$year)
## [1] 2002

2. How do these counts compare to Arbuthnot’s? Are they on a similar scale?

Answer: The counts here are in millions vs Arbuthmot’s is in thousands.

present
##    year    boys   girls
## 1  1940 1211684 1148715
## 2  1941 1289734 1223693
## 3  1942 1444365 1364631
## 4  1943 1508959 1427901
## 5  1944 1435301 1359499
## 6  1945 1404587 1330869
## 7  1946 1691220 1597452
## 8  1947 1899876 1800064
## 9  1948 1813852 1721216
## 10 1949 1826352 1733177
## 11 1950 1823555 1730594
## 12 1951 1923020 1827830
## 13 1952 1971262 1875724
## 14 1953 2001798 1900322
## 15 1954 2059068 1958294
## 16 1955 2073719 1973576
## 17 1956 2133588 2029502
## 18 1957 2179960 2074824
## 19 1958 2152546 2051266
## 20 1959 2173638 2071158
## 21 1960 2179708 2078142
## 22 1961 2186274 2082052
## 23 1962 2132466 2034896
## 24 1963 2101632 1996388
## 25 1964 2060162 1967328
## 26 1965 1927054 1833304
## 27 1966 1845862 1760412
## 28 1967 1803388 1717571
## 29 1968 1796326 1705238
## 30 1969 1846572 1753634
## 31 1970 1915378 1816008
## 32 1971 1822910 1733060
## 33 1972 1669927 1588484
## 34 1973 1608326 1528639
## 35 1974 1622114 1537844
## 36 1975 1613135 1531063
## 37 1976 1624436 1543352
## 38 1977 1705916 1620716
## 39 1978 1709394 1623885
## 40 1979 1791267 1703131
## 41 1980 1852616 1759642
## 42 1981 1860272 1768966
## 43 1982 1885676 1794861
## 44 1983 1865553 1773380
## 45 1984 1879490 1789651
## 46 1985 1927983 1832578
## 47 1986 1924868 1831679
## 48 1987 1951153 1858241
## 49 1988 2002424 1907086
## 50 1989 2069490 1971468
## 51 1990 2129495 2028717
## 52 1991 2101518 2009389
## 53 1992 2082097 1982917
## 54 1993 2048861 1951379
## 55 1994 2022589 1930178
## 56 1995 1996355 1903234
## 57 1996 1990480 1901014
## 58 1997 1985596 1895298
## 59 1998 2016205 1925348
## 60 1999 2026854 1932563
## 61 2000 2076969 1981845
## 62 2001 2057922 1968011
## 63 2002 2057979 1963747

3. Make a plot that displays the boy-to-girl ratio for every year in the data set. What do you see? Does Arbuthnot’s observation about boys being born in greater proportion than girls hold up in the U.S.? Include the plot in your response.

Answer: Yes the ratio of boys being born is greater proportion though over time it is converging.

plot(present$year, present$boys / (present$boys + present$girls), type = "l")

plot(present$year, present$girls / (present$boys + present$girls), type = "l")

4. In what year did we see the most total number of births in the U.S.? You can refer to the help files or the R reference card http://cran.r-project.org/doc/contrib/Short-refcard.pdf to find helpful commands.

Answer: 1961

which.max(present$boys + present$girls)
## [1] 22
print(present$year[22])
## [1] 1961