The number of seeds per fruit for the freshwater plan Vallis

The number of seeds per fruit for the freshwater plan Vallisneria Americana varies considerably from one fruit to another. A researcher took a random sample of 12 fruit and found that the average number of seeds was 320, with a sample standard deviation of 125. The researcher expected the number of seeds to follow, at least approximately, a normal distribution. Find the LOWER limit of a 95% confidence interval for the population mean.

1. 249.27

2. 240.58

3. 242.56

4. 241.38

Solution

Note that              
      
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
      
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    320          
t(alpha/2) = critical t for the confidence interval =    2.20098516          
s = sample standard deviation =    125          
n = sample size =    12          
df = n - 1 =    11          

Thus,              

Lower bound =    240.5787891 = 240.58 [ANSWER, OPTION 2]