PLEASE SHOW ALL WORK A poll asked a national random sample o

PLEASE SHOW ALL WORK

A poll asked a national random sample of 501 adult women to state their current weight. The mean weight in the sample was = 153. We will treat these data as an SRS from a Normally distributed population with standard deviation sigma = 32. Give a 95% confidence interval for the mean weight of adult women based on these data. (Round your answers to two decimal places.) Do you trust the interval you computed in part (a) as a 95% confidence interval for the mean weight of all U.S. adult women? Why or why not? Yes, because the sample is an SRS and the central limit theorem applies. Yes, because the sample size was large. No, because the women may have under or over estimated their weight. No, because the sample is not representative of all adult women. You may need to use the appropriate Appendix Table to answer this question.

Solution

A)

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    153          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    32          
n = sample size =    501          
              
Thus,              
              
Lower bound =    150.1979285          
Upper bound =    155.8020715          
              
Thus, the confidence interval is              
              
(   150.1979285   ,   155.8020715   ) [ANSWER]

B)

Yes, because the sample is an SRS and the central limit theorem applies. [ANSWER, OPTION A]