Question

According to the National Health Statistics Reports, the standard deviation of the weights of all one-year-old baby boys born in the U.S. is 5.3 pounds. A random sample of 360 one-year-old baby boys born in the U.S. had a mean weight of 25.5 pounds.

a) Construct a 90% confidence interval for the mean weight of all one-year-old baby boys in the U.S. Write a sentence that interprets this interval.

b) Should this confidence interval be used to estimate the mean weights of all one-year-old babies in the U.S.? Explain.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 25.5

Population standard deviation =    = 5.3

Sample size = n =360

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.645* (5.3 /  360 )

= 0.4595
At 90% confidence interval estimate of the population mean
is,

- E < < + E

25.5 - 0.4595 <   < 25.5 + 0.4595

25.0405 <   < 25.9595

( 25.0405 , 25.9595 )

At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )