Question

Important instructions: For all situations requiring a hypothesis test (z test, one-samplet test, one-sample variance test or two-sample t test), you must 1. Choose the appropriate test based on the information you are given 2. State null and alternative hypotheses 3. Choose a one or two tailed test and explain why you chose that test 4. Calculate the appropriate test statistic, showing all work neatly. This includes calculations of means, standard deviations, etc. 5. Draw the appropriate conclusions (i.e., do you reject or fail to reject Ho?) To help you know for sure which questions require this, I have marked the questions requiring these steps with an asterisk (*).You may assume data are normal and have equal variances-that necessary assumptions have been fulfilled.

Answer 1

1) two sample t test with equal variance

2)

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

3) two tail test, because alternative hypothesis is non directional

4) Sample #1   ---->   1                  
mean of sample 1,    x̅1=   5.590                  
standard deviation of sample 1,   s1 =    0.742                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   4.411                  
standard deviation of sample 2,   s2 =    1.034                  
size of sample 2,    n2=   9                  
                          
difference in sample means =    x̅1-x̅2 =    5.5900   -   4.4   =   1.179  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    0.8911                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.4094                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   1.1789   -   0   ) /    0.41 =   2.8794

5)

Degree of freedom, DF=   n1+n2-2 =    17  
p-value =        0.010406 (excel function: =T.DIST.2T(t stat,df) )
Conclusion:     p-value <α , Reject null hypothesis     

There is enough evidence that two breeds differ in sensitivity at α=0.05