The world population of Whooping Cranes is now 237 theyre co

The world population of Whooping Cranes is now 237, they\'re coming back from an all-time low of 15 birds. The average egg of a Whooping Crane is 208 grams, but a new batch of nine eggs had the weights listed below (in grams). Test whether or not the new hatch has larger than average eggs at the 99% confidence level.

210   208.5   211.6   212   210.3   210.2   209   206.4   209.7

Give a statistically appropriate conclusion to the hypothesis test

Solution

Getting the means and standard deviation of the sample,

Xbar = 209.7444444
s = 1.673403053

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   208
Ha:    u   >   208
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical t,          
df = n - 1 =    8      
tcrit =    2.896459448      
          
Getting the test statistic, as          
          
X = sample mean =    209.7444444      
uo = hypothesized mean =    208      
n = sample size =    9      
s = standard deviation =    1.673403053      
          
Thus, t = (X - uo) * sqrt(n) / s =    3.127359658      
          
Also, the p value is          
          
p =    0.00703565      
          
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.      

Thus, we have sufficient evidence at 99% confidence that this new batch of eggs is larger than the avergae of 208 g. [ANSWER]