Using the simple random sample of weights of women from a da

Using the simple random sample of weights of women from a data set, we obtain these sample statistics: n=35 and x=153.78 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by =30.92 lb.

a. Find the best point estimate of the mean weight of all women.

The best estimate is ____ lb

b. Find a 95% confidence interval estimate of the mean weight of all women.

The 95% confidence interval estimate is ____ lb < < ______ lb

Solution

a)

It is the sample mean, 153.78 lb. [ANSWER]

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
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 =    153.78          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    30.92          
n = sample size =    35          
              
Thus,              
Margin of Error E =    10.24362223          
Lower bound =    143.5363778          
Upper bound =    164.0236222          
              
Thus, the confidence interval is              
              
(   143.5363778   ,   164.0236222   ) [ANSWER]