The mean weight of newborn infants at a community hospital is said to be 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. Does this sample support the original claim? What is the decision for a significant increase in the average birthrate at a 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 lower than 6.6 lb.
C) Reject the null hypothesis and conclude the mean is greater than 6.6 lb.
D) Cannot calculate because population standard deviation is unknown.

Question

The mean weight of newborn infants at a community hospital is said to be 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. Does this sample support the original claim? What is the decision for a significant increase in the average birthrate at a 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 lower than 6.6 lb. 
C) Reject the null hypothesis and conclude the mean is greater than 6.6 lb. 
D) Cannot calculate because population standard deviation is unknown.

Quizplus · Accepted Answer

We can use a one-sample t-test to compare the sample mean to the population mean. The null hypothesis is that the mean weight of newborn infants is 6.6 pounds, and the alternative hypothesis is that it is greater than 6.6 pounds. Using a t-test with 6 degrees of freedom, we find a test statistic of 2.28 and a p-value of 0.03. At a 5% level of significance, this is statistically significant evidence to reject the null hypothesis and conclude that the mean weight of newborn infants is greater than 6.6 pounds. Therefore, the best choice is C.

The Mean Weight of Newborn Infants at a Community Hospital