Posted: November 26th, 2016
1- The data of a large survey (n=1200) in Cairo in 2010 yielded the following graph regarding the birth weight of newborns. Sample mean () and standard deviation (Sd) are given in the graph:
Using the data in the graph, calculate the probability that a newborn has a birth weight between 2000 g and 3000 g (2000 g < birth weight < 3000 g).
b) Calculate the probability that a newborn has a birth weight larger than 4000 g.
2- In that large-scale survey, the investigators realized that the number of mothers of 19 years and under is very low. In order to correctly estimate the mean birth weight of infants to these mothers, the investigators thought to recruit more mothers of age 19 and under.
Taking into consideration the following: the mean birth weight of infants for the mothers in the sample with age ≤19 years is 2833.33 grams with a standard deviation of 301.11 grams.
Using this estimate of the mean, how many women 19 years of age and under must be enrolled in the study to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a margin of error not exceeding 50 grams?
3- Suppose a researcher wants to assess if there is a significant difference between the birthweight of newborns of working mothers and that of newborns of non-working mothers.
Using the data in the provided data set:
For housewives: n= 12; average birthweight of their newborns =3037.5 g; and standard deviation s=166.69 g. (Mothers with abortions or stillbirths are excluded)
For working mothers: n=14; average birthweight of their newborns =2546.43 g; and standard deviation s=326.68 g. (Mothers with abortions or stillbirths are excluded)
Is there enough statistical evidence to support the claim that the mean birthweight of newborns of housewives is significantly different from that of working mothers?
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