Question: If the 95% confidence interval for the mean weight of infants born to mothers who smoke is found to be 5.3 pounds to 6.5 pounds using the formula \[\overset{\_}{\mathop{x}}\,\pm {{z}_{1-\frac{\alpha }{2}}}\frac{\sigma }{\sqrt{n}}\].

a. What is the value of the sample mean used to calculate the confidence interval?

b. What is margin of error of the confidence interval?

c. What is the standard error of the estimate?

d. Calculate the 99% confidence interval for μ.

e. The sample mean is significantly different from 7.2 pounds at α = 0.05. Is the difference significant at α = 0.01?