Question

A recent study revealed that the average weight of babies born in the United States is normally distributed with a mean of 7.5 pounds. This number is lower than recent years and so researchers are interested in determining what factors are associated with lower birth weights. One researcher decides to look at the age of the mother to determine if younger mothers have babies that are significantly heavier or lighter than average. To study this the researcher collects data from 87 babies who were born to mothers between the ages of 16 and 18. Only one baby was measured per mother. Twins and other multiple births were excluded. The average weight for these babies was 7.3 pounds with a standard deviation of .6 pounds.

Which of the following statements is relevant to the assumption of Normality?

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population
b. only one baby was measured per mother
c. weights of babies are normally distributed in the population
d. the study used a sample that is different than the comparison population and measured weight on a ratio scale

Answer 1

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population

Explanation:

The population mean = μ= 7.5

Sample mean = x`= 7.3

Sample standard deviation= s= 0.6

Sample size = 87

Assuming normality we perform z test

z= x`-u/s/√n

z= 7.3-7.5/0.6/√87

z= -3.11

The critical region for 0.05 for two tailed test is z>+1.96 and Z<-1.96

Since the calculated z= -3.11 falls in the critical region Z<-1.96 we conclude that birth rate is lower in the young mothers.

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population

Only choice a is correct because when n > 30 the population standard deviation and the sample standard deviation are assumed to be normal

Choice b cannot be the correct option because it is already inferred that only one baby was measured per mother.

Choice C cannot be also the best choice because it is already assumed.

Choice d is totally incorrect.