A species of bats is being studied A sample of 40 bats has s

A species of bats is being studied. A sample of 40 bats has sample mean x = 4.75gm. Let x be a random variable of population bat weights, normally distributed, with sigma =.70 gm and mu = 5.55 gm. Do the date indicate that the mean weight of the bats is less than 5.55gm? Use alpha =.01.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   5.55  
Ha:    u   <   5.55  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    4.75          
uo = hypothesized mean =    5.55          
n = sample size =    40          
s = standard deviation =    0.7          
              
Thus, z = (X - uo) * sqrt(n) / s =    -7.228063223          
              
Also, the p value is              
              
p =    2.44965*10^-13          
              
As |z| > 2.326, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the mean weight of the bats is less than 5.55 gm at 0.01 level. [CONCLUSION]