download.file("http://www.openintro.org/stat/data/nc.RData", destfile = "nc.RData")
load("nc.RData")
Ex 1, What are the cases in this data set? How many cases are there in our sample?
summary(nc)
## fage mage mature weeks
## Min. :14.00 Min. :13 mature mom :133 Min. :20.00
## 1st Qu.:25.00 1st Qu.:22 younger mom:867 1st Qu.:37.00
## Median :30.00 Median :27 Median :39.00
## Mean :30.26 Mean :27 Mean :38.33
## 3rd Qu.:35.00 3rd Qu.:32 3rd Qu.:40.00
## Max. :55.00 Max. :50 Max. :45.00
## NA's :171 NA's :2
## premie visits marital gained
## full term:846 Min. : 0.0 married :386 Min. : 0.00
## premie :152 1st Qu.:10.0 not married:613 1st Qu.:20.00
## NA's : 2 Median :12.0 NA's : 1 Median :30.00
## Mean :12.1 Mean :30.33
## 3rd Qu.:15.0 3rd Qu.:38.00
## Max. :30.0 Max. :85.00
## NA's :9 NA's :27
## weight lowbirthweight gender habit
## Min. : 1.000 low :111 female:503 nonsmoker:873
## 1st Qu.: 6.380 not low:889 male :497 smoker :126
## Median : 7.310 NA's : 1
## Mean : 7.101
## 3rd Qu.: 8.060
## Max. :11.750
##
## whitemom
## not white:284
## white :714
## NA's : 2
##
##
##
##
Ex 2, Make a side-by-side boxplot of habit and weight. What does the plot highlight about the relationship between these two variables?
by(nc$weight, nc$habit, mean)
## nc$habit: nonsmoker
## [1] 7.144273
## --------------------------------------------------------
## nc$habit: smoker
## [1] 6.82873
Ex 3, Check if the conditions necessary for inference are satisfied. Note that you will need to obtain sample sizes to check the conditions. You can compute the group size using the same by command above but replacing mean with length.
by(nc$weight, nc$habit, length)
## nc$habit: nonsmoker
## [1] 873
## --------------------------------------------------------
## nc$habit: smoker
## [1] 126
Ex 4, Write the hypotheses for testing if the average weights of babies born to smoking and non-smoking mothers are different.
inference(y = nc$weight, x = nc$habit, est = "mean", type = "ht", null = 0,
alternative = "twosided", method = "theoretical")
## Warning: package 'BHH2' was built under R version 3.5.3
## Response variable: numerical, Explanatory variable: categorical
## Difference between two means
## Summary statistics:
## n_nonsmoker = 873, mean_nonsmoker = 7.1443, sd_nonsmoker = 1.5187
## n_smoker = 126, mean_smoker = 6.8287, sd_smoker = 1.3862
## Observed difference between means (nonsmoker-smoker) = 0.3155
##
## H0: mu_nonsmoker - mu_smoker = 0
## HA: mu_nonsmoker - mu_smoker != 0
## Standard error = 0.134
## Test statistic: Z = 2.359
## p-value = 0.0184
Ex 5, Change the type argument to “ci” to construct and record a confidence interval for the difference between the weights of babies born to smoking and non-smoking mothers.
inference(y = nc$weight, x = nc$habit, est = "mean", type = "ci", null = 0,
alternative = "twosided", method = "theoretical",
order = c("smoker","nonsmoker"))
## Response variable: numerical, Explanatory variable: categorical
## Difference between two means
## Summary statistics:
## n_smoker = 126, mean_smoker = 6.8287, sd_smoker = 1.3862
## n_nonsmoker = 873, mean_nonsmoker = 7.1443, sd_nonsmoker = 1.5187
## Observed difference between means (smoker-nonsmoker) = -0.3155
##
## Standard error = 0.1338
## 95 % Confidence interval = ( -0.5777 , -0.0534 )
On Your Own
1, Calculate a 95% confidence interval for the average length of pregnancies (weeks) and interpret it in context. Note that since you’re doing inference on a single population parameter, there is no explanatory variable, so you can omit the x variable from the function.
inference(y = nc$weeks, est = "mean", type = "ci",
alternative = "twosided", method = "theoretical")
## Single mean
## Summary statistics:
## mean = 38.3347 ; sd = 2.9316 ; n = 998
## Standard error = 0.0928
## 95 % Confidence interval = ( 38.1528 , 38.5165 )
2, Calculate a new confidence interval for the same parameter at the 90% confidence level. You can change the confidence level by adding a new argument to the function: conflevel = 0.90.
inference(y = nc$weeks, est = "mean", type = "ci", confleve = 0.90,
alternative = "twosided", method = "theoretical")
## Single mean
## Summary statistics:
## mean = 38.3347 ; sd = 2.9316 ; n = 998
## Standard error = 0.0928
## 90 % Confidence interval = ( 38.182 , 38.4873 )
3, Conduct a hypothesis test evaluating whether the average weight gained by younger mothers is different than the average weight gained by mature mothers.
inference(y = nc$gained, x = nc$mature, est = "mean", type = "ht", null = 0,
alternative = "twosided", method = "theoretical",
order = c("mature mom", "younger mom"))
## Response variable: numerical, Explanatory variable: categorical
## Difference between two means
## Summary statistics:
## n_mature mom = 129, mean_mature mom = 28.7907, sd_mature mom = 13.4824
## n_younger mom = 844, mean_younger mom = 30.5604, sd_younger mom = 14.3469
## Observed difference between means (mature mom-younger mom) = -1.7697
##
## H0: mu_mature mom - mu_younger mom = 0
## HA: mu_mature mom - mu_younger mom != 0
## Standard error = 1.286
## Test statistic: Z = -1.376
## p-value = 0.1686
4, Now, a non-inference task: Determine the age cutoff for younger and mature mothers. Use a method of your choice, and explain how your method works.
young.mom <- subset(nc, nc$mature == "younger mom")
mature.mom <- subset(nc, nc$mature == "mature mom")
summary(young.mom)
## fage mage mature weeks
## Min. :14.00 Min. :13.00 mature mom : 0 Min. :22.00
## 1st Qu.:24.00 1st Qu.:21.00 younger mom:867 1st Qu.:37.00
## Median :29.00 Median :25.00 Median :39.00
## Mean :28.86 Mean :25.44 Mean :38.38
## 3rd Qu.:33.00 3rd Qu.:30.00 3rd Qu.:40.00
## Max. :48.00 Max. :34.00 Max. :45.00
## NA's :160 NA's :1
## premie visits marital gained
## full term:737 Min. : 0.00 married :361 Min. : 0.00
## premie :129 1st Qu.:10.00 not married:506 1st Qu.:21.00
## NA's : 1 Median :12.00 Median :30.00
## Mean :12.03 Mean :30.56
## 3rd Qu.:15.00 3rd Qu.:38.25
## Max. :30.00 Max. :85.00
## NA's :7 NA's :23
## weight lowbirthweight gender habit
## Min. : 1.000 low : 93 female:435 nonsmoker:752
## 1st Qu.: 6.380 not low:774 male :432 smoker :115
## Median : 7.310
## Mean : 7.097
## 3rd Qu.: 8.000
## Max. :11.750
##
## whitemom
## not white:255
## white :611
## NA's : 1
##
##
##
##
summary(mature.mom)
## fage mage mature weeks
## Min. :26.00 Min. :35.00 mature mom :133 Min. :20.00
## 1st Qu.:35.00 1st Qu.:35.00 younger mom: 0 1st Qu.:38.00
## Median :38.00 Median :37.00 Median :39.00
## Mean :38.36 Mean :37.18 Mean :38.02
## 3rd Qu.:41.00 3rd Qu.:38.00 3rd Qu.:40.00
## Max. :55.00 Max. :50.00 Max. :44.00
## NA's :11 NA's :1
## premie visits marital gained
## full term:109 Min. : 3.00 married : 25 Min. : 0.00
## premie : 23 1st Qu.:10.00 not married:107 1st Qu.:20.00
## NA's : 1 Median :12.00 NA's : 1 Median :28.00
## Mean :12.61 Mean :28.79
## 3rd Qu.:15.00 3rd Qu.:36.00
## Max. :30.00 Max. :70.00
## NA's :2 NA's :4
## weight lowbirthweight gender habit
## Min. : 1.380 low : 18 female:68 nonsmoker:121
## 1st Qu.: 6.380 not low:115 male :65 smoker : 11
## Median : 7.310 NA's : 1
## Mean : 7.126
## 3rd Qu.: 8.190
## Max. :10.250
##
## whitemom
## not white: 29
## white :103
## NA's : 1
##
##
##
##
mom <- c(young.mom, mature.mom)
hist(mature.mom$mage, breaks = 20, xlim = c(10,50))
hist(young.mom$mage, breaks = 20, xlim = c(10,50))
