Question

Birth Weights

The distribution of birth weights (in grams) for all children who shared multiple births (twins, triplets, etc.) in North Carolina during 2007 was as shown in the table below Weight (in grams) 0-500 501-1500 1501-2500 2501-8165 Percentage of children1.6812.07 47.39 38.86 The frequency distribution of birth weights of a sample of 200 children who shared multiple births and were born in North Carolina in 2009 was as shown in the following table. Weight (in grams) 0-500 501-1500 1501-2500 2501-8165 Percentage of children2 73 103 Test at the 5% significance level whether the 2009 distribution of birth weights for all children born in North Carolina who shared multiple births is significantly different from the one for 2007.

Answer 1

null hypothesis, HO: there is no significant difference in the average birth weight of all children born in North Carolina in the year 2007 and 2009.

alternative hypothesis, H1: there is a significant difference in the average birth weight of all children born in North Carolina in the year 2007 and 2009.

part1	part2	di
1.68	2	-0.32
12.07	22	-9.93
47.39	73	-25.61
38.86	103	-64.14

mean_diff= -25 [Excel function used -> AVERAGE]

sd_diff= 28.098 [Excel function used -> STDEV]

n= 4 [Excel function used -> COUNT]

t= (mean_diff)/(sd_diff/sqrt(n))

t= -25/(28.0982/sqrt(4))

t= -1.7795

alpha= 0.05

critical value, t(a/2,n-1) =t(0.05/2,4-1) =t.INV.2T(0.05,4-1) = 3.182

p-value = 2*(1-P(T<|t|)

p-value = 2*(1-P(T<abs(-1.77947341822608))

p-value = T.DIST.2T(abs(-1.77947341822608),4-1)

p-value = 0.173

With (t=-1.7795, p<5%), I reject the null hypothesis at 5% level of significance. There is sufficient evidence to conclude that there is a significant difference in the average birth weight of all children born in North Carolina in the year 2007 and 2009.