This is for R (RStudio). This is how the dataset looks like for \"birthwt\" > bi

Question

This is for R (RStudio).

This is how the dataset looks like for "birthwt"

> birthwt
low age lwt race smoke ptl ht ui ftv bwt
85 0 19 182 2 0 0 0 1 0 2523
86 0 33 155 3 0 0 0 0 3 2551
87 0 20 105 1 1 0 0 0 1 2557
88 0 21 108 1 1 0 0 1 2 2594
89 0 18 107 1 1 0 0 1 0 2600
91 0 21 124 3 0 0 0 0 0 2622
92 0 22 118 1 0 0 0 0 1 2637
93 0 17 103 3 0 0 0 0 1 2637
94 0 29 123 1 1 0 0 0 1 2663
95 0 26 113 1 1 0 0 0 0 2665
96 0 19 95 3 0 0 0 0 0 2722
97 0 19 150 3 0 0 0 0 1 2733
98 0 22 95 3 0 0 1 0 0 2751
99 0 30 107 3 0 1 0 1 2 2750
100 0 18 100 1 1 0 0 0 0 2769
101 0 18 100 1 1 0 0 0 0 2769
102 0 15 98 2 0 0 0 0 0 2778
103 0 25 118 1 1 0 0 0 3 2782
104 0 20 120 3 0 0 0 1 0 2807
105 0 28 120 1 1 0 0 0 1 2821
106 0 32 121 3 0 0 0 0 2 2835
107 0 31 100 1 0 0 0 1 3 2835
108 0 36 202 1 0 0 0 0 1 2836
109 0 28 120 3 0 0 0 0 0 2863
111 0 25 120 3 0 0 0 1 2 2877
112 0 28 167 1 0 0 0 0 0 2877
113 0 17 122 1 1 0 0 0 0 2906
114 0 29 150 1 0 0 0 0 2 2920
115 0 26 168 2 1 0 0 0 0 2920
116 0 17 113 2 0 0 0 0 1 2920
117 0 17 113 2 0 0 0 0 1 2920
118 0 24 90 1 1 1 0 0 1 2948
119 0 35 121 2 1 1 0 0 1 2948
120 0 25 155 1 0 0 0 0 1 2977
121 0 25 125 2 0 0 0 0 0 2977
123 0 29 140 1 1 0 0 0 2 2977
124 0 19 138 1 1 0 0 0 2 2977
125 0 27 124 1 1 0 0 0 0 2922
126 0 31 215 1 1 0 0 0 2 3005
127 0 33 109 1 1 0 0 0 1 3033
128 0 21 185 2 1 0 0 0 2 3042
129 0 19 189 1 0 0 0 0 2 3062
130 0 23 130 2 0 0 0 0 1 3062
131 0 21 160 1 0 0 0 0 0 3062
132 0 18 90 1 1 0 0 1 0 3062
133 0 18 90 1 1 0 0 1 0 3062
134 0 32 132 1 0 0 0 0 4 3080
135 0 19 132 3 0 0 0 0 0 3090
136 0 24 115 1 0 0 0 0 2 3090
137 0 22 85 3 1 0 0 0 0 3090
138 0 22 120 1 0 0 1 0 1 3100
139 0 23 128 3 0 0 0 0 0 3104
140 0 22 130 1 1 0 0 0 0 3132
141 0 30 95 1 1 0 0 0 2 3147
142 0 19 115 3 0 0 0 0 0 3175
143 0 16 110 3 0 0 0 0 0 3175
144 0 21 110 3 1 0 0 1 0 3203
145 0 30 153 3 0 0 0 0 0 3203
146 0 20 103 3 0 0 0 0 0 3203
147 0 17 119 3 0 0 0 0 0 3225
148 0 17 119 3 0 0 0 0 0 3225
149 0 23 119 3 0 0 0 0 2 3232
150 0 24 110 3 0 0 0 0 0 3232
151 0 28 140 1 0 0 0 0 0 3234
154 0 26 133 3 1 2 0 0 0 3260
155 0 20 169 3 0 1 0 1 1 3274
156 0 24 115 3 0 0 0 0 2 3274
159 0 28 250 3 1 0 0 0 6 3303
160 0 20 141 1 0 2 0 1 1 3317
161 0 22 158 2 0 1 0 0 2 3317
162 0 22 112 1 1 2 0 0 0 3317
163 0 31 150 3 1 0 0 0 2 3321
164 0 23 115 3 1 0 0 0 1 3331
166 0 16 112 2 0 0 0 0 0 3374
167 0 16 135 1 1 0 0 0 0 3374
168 0 18 229 2 0 0 0 0 0 3402
169 0 25 140 1 0 0 0 0 1 3416
170 0 32 134 1 1 1 0 0 4 3430
172 0 20 121 2 1 0 0 0 0 3444
173 0 23 190 1 0 0 0 0 0 3459
174 0 22 131 1 0 0 0 0 1 3460
175 0 32 170 1 0 0 0 0 0 3473
176 0 30 110 3 0 0 0 0 0 3544
177 0 20 127 3 0 0 0 0 0 3487
179 0 23 123 3 0 0 0 0 0 3544
180 0 17 120 3 1 0 0 0 0 3572
181 0 19 105 3 0 0 0 0 0 3572
182 0 23 130 1 0 0 0 0 0 3586
183 0 36 175 1 0 0 0 0 0 3600
184 0 22 125 1 0 0 0 0 1 3614
185 0 24 133 1 0 0 0 0 0 3614
186 0 21 134 3 0 0 0 0 2 3629
187 0 19 235 1 1 0 1 0 0 3629
188 0 25 95 1 1 3 0 1 0 3637
189 0 16 135 1 1 0 0 0 0 3643
190 0 29 135 1 0 0 0 0 1 3651
191 0 29 154 1 0 0 0 0 1 3651
192 0 19 147 1 1 0 0 0 0 3651
193 0 19 147 1 1 0 0 0 0 3651
195 0 30 137 1 0 0 0 0 1 3699
[ reached getOption("max.print") -- omitted 89 rows ]

For this problem, we will return to the birthwt dataset. We are interested in determining whether or not the birth weight of children born to mothers who smoke is different from the birth weight of children born to mothers who do not smoke. Assume that the population standard deviations are different and unknown. Recall that in the dataset, the bwt column contains the baby's weight and smoke is a categorical variable which equals 1 if the mother smokes and 0 if they do not 1. Write down the null and alternative hypotheses. Be sure to define any parameters you use 2. What is sample mean birth weight for children born to smokers? What is it for children born to non-smokers? 3. What is the the sample standard deviation birth weight for children born to smokers? What is it for children born to non-smokers? 4. What is the value of the test statistic you will use to check the null hypothesis? 5. What is the p-value of the test statistic? 6. Construct a 99% confidence interval for the difference in mean birth weight. Does this interval contain 0? 7. What is your statistical decision? Use = 01. 8. What is your real-world decision?

Explanation / Answer

The complete R snippet is as follows

library(MASS)
data("birthwt")
birthwt
names(birthwt)

smoke<-subset(birthwt, birthwt$smoke=="1")
nosmoke<-subset(birthwt,birthwt$smoke=="0")

t.test(smoke$bwt,nosmoke$bwt,conf.level = 0.99)

## means
mean(smoke$bwt)
mean(nosmoke$bwt)

## sd
sd(smoke$bwt)
sd(nosmoke$bwt)

The results are

t.test(smoke$bwt,nosmoke$bwt,conf.level = 0.99)

   Welch Two Sample t-test

data: smoke$bwt and nosmoke$bwt
t = -2.7299, df = 170.1, p-value = 0.007003 ## as this is less than 0.01 , hence we reject the null hypothesis in favor of alternate hypothesis
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-554.57562 -12.97784 , the difference does not include zero
sample estimates:
mean of x mean of y
2771.919 3055.696

H0 : The mean values of bwt are equal

H1 : The mean values of bwt are not equal

Other stats of interest are

## means
> mean(smoke$bwt)
[1] 2771.919
> mean(nosmoke$bwt)
[1] 3055.696
>
> ## sd
> sd(smoke$bwt)
[1] 659.6349
> sd(nosmoke$bwt)
[1] 752.6566

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