Question

According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.

1. Construct a 99% confidence interval for the mean weight of one-year-old baby boys in the United States.
2. Based on this confidence interval, is it likely that the mean weight of all one-year-old boys is less than 28 pounds?

Answer 1

a)

99% Confidence Interval :-   
X̅ ± Z( α /2) σ / √ ( n )  
Z(α/2) = Z (0.01 /2) = 2.576 (From Z table)
25.5 ± 2.576 * 5.3/√(360)  
Lower Limit = 25.5 - 2.576 * 5.3/√(360)  
Lower Limit = 24.78   
Upper Limit = 25.5 + 2.576 * 5.3/√(360)  
Upper Limit = 26.22  
99% Confidence interval is ( 24.78 , 26.212)   

b)

Since all values in confidence interval are less than 28, we have sufficient evidence to
conclude that the mean weight of all one-year-old boys is less than 28 pounds