Question

2. Corn plants grow to a mean height of 6.43 feet with a standard deviation of 0.14 feet. A new genetically modified corn plant is being developed. A researcher grew a group of 37 genetically modified corn plants and found that their mean height was 6.52 feet. Test to determine if the genetically modified plants are taller using α = 0.01.

Answer 1

To Test :-

H0 :-  $\mu<=6.43$

H1 :- $\mu>6.43$

Test Statistic :-                                   
$Z = ( X - \mu ) / ( \sigma / \sqrt{n})$
$Z = ( 6.52 - 6.43 ) / ( 0.14 /\sqrt{ 37 })$                                
Z = 3.9103

                               
Test Criteria :-                                    
Reject null hypothesis if $Z \; > \; Z_{\alpha}$
$Z_{\alpha} = Z_{ 0.01 } = 2.33$                                
$Z \; > \; Z_{\alpha } = 3.9103 > 2.33$                            
Result :- Reject null hypothesis       

Conclusion :- Accept Alternative Hypothesis

$\mu>6.43$

There is sufficient evidence to support the claim that  genetically modified plants are taller at α = 0.01 level of significance.