The mean weight of newborn infants at a community hospital 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. Does the sample data show 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 pounds.
B)Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.
C)Reject the null hypothesis and conclude the mean is greater than 6.6 pounds.
D)Cannot calculate because the population standard deviation is unknown.

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test because the population standard deviation is unknown. The null hypothesis is that the population mean weight is 6.6 pounds and the alternative hypothesis is that the population mean weight is greater than 6.6 pounds. Using a t-test with six degrees of freedom (n-1=7-1=6) and a significance level of 0.05, we find that the t-statistic is 1.992 and the p-value is 0.046. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the sample data shows a significant increase in the average birthrate. Therefore, the best choice is C: Reject the null hypothesis and conclude the mean is greater than 6.6 pounds.

The Mean Weight of Newborn Infants at a Community Hospital