A hospital researcher wishes to estimate the mean weight of full-term newborns.

Question

A hospital researcher wishes to estimate the mean weight of full-term newborns. A random sample of 13 full-term newborns had a mean birthweight of 7.3 pounds with a standard deviation of 2.2 pounds. Compute a 95% confidence interval for the mean weight of all full-term newborns.

Suppose the national average birthweight of full-term newborns is 9 pounds. Does evidence suggest that the mean birthweight amongst the newborns in the study above is lower? Conduct the appropriate hypothesis test, report a p value and interpret.

Explanation / Answer

sample mean = 7.3 and std. dev. = 2.2
For 95% CI, t-value for 12 degrees of freedom is 2.179

lower limit = 7.3 - 2.179*2.2/sqrt(13) = 5.9704
upper limit = 7.3 + 2.179*2.2/sqrt(13) = 8.6296

Below are the null and alternate hypothesis
H0: mu >= 9
H1: mu < 9

value of test statistics, t = (7.3 - 9)/(2.2/sqrt(13)) = -2.7861

p-value = 0.008232

As p-value is less than significance level of 0.05, we reject the null hypothesis.
This means evidence suggests that the mean birth weight amongs the newborns in the study is lower.

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