Question

In: Statistics and Probability

A researcher investigated the effects of green and red light on the growth rate of bean...

A researcher investigated the effects of green and red light on the growth rate of bean plants.  The table below summarizes the heights (in inches) of bean plants from soil to first branching stem.  

Light

Sample Mean

Sample Standard Deviation

Sample Size

Red

8.36

1.50

17

Green

8.94

2.78

25

(A – 10 pts.)  Use the Pooled two-sample t-procedure to construct the 95% confidence interval for the difference in mean height for bean plants exposed to these two colors of light.  (You do not need to interpret the confidence interval.)

(B – 8 pts.)  Suppose that you wish to address the question of whether mean height differs for bean plants exposed to these two colors of light.  State the null hypothesis and the alternative hypothesis, using appropriate notation. Clearly identify what each symbol represents.  Do not attempt to conduct the test.

Solutions

Expert Solution

a)

Degree of freedom, DF=   n1+n2-2 =    40              
t-critical value =    t α/2 =    2.0211   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.3531              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    0.7397              
margin of error, E = t*SE =    2.0211   *   0.7397   =   1.4950  
                      
difference of means =    x̅1-x̅2 =    8.3600   -   8.940   =   -0.5800
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    -0.5800   -   1.4950   =   -2.0750
Interval Upper Limit=   (x̅1-x̅2) + E =    -0.5800   +   1.4950   =   0.9150

b)

Ho : Difference between Mean height for bean plants exposed to these Red colors of light and Mean height for bean plants exposed to these green colors of light is zero

Ha : Difference between Mean height for bean plants exposed to these Red colors of light and Mean height for bean plants exposed to these green colors of light is not equal to zero

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0

THANKS

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orchestra answered 11 months ago
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