A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?
A) Fail to reject the null hypothesis and conclude the mean is 6.6 lb.
B) Reject the null hypothesis and conclude the mean is higher than 6.6 lb.
C) Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
D) Cannot calculate because population standard deviation is unknown.

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean weight of newborn infants is 6.6 lbs. The alternative hypothesis is that the mean is different from 6.6 lbs. 
Using a two-tailed t-test with a significance level of 0.05 and degrees of freedom of 6, the critical values are ±2.447. 
We calculate the sample mean to be 7.7 lbs and the sample standard deviation to be 1.288 lbs. 
The t statistic is (7.7 - 6.6)/(1.288/sqrt(7)) = 2.26.
Since the absolute value of the t-statistic is less than the critical value of 2.447, we fail to reject the null hypothesis at the 5% level of significance. Therefore, we can conclude that there is not enough evidence to support a statistical significant change in average weights at birth at the 5% level of significance, and that the mean weight of newborn infants is likely 6.6 lbs.

A Hypothesis Regarding the Weight of Newborn Infants at a Community