Which of the following are dependent samples: (a) older siblings; younger siblings | Solution

1. Which of the following are dependent samples:                             
    (a) older siblings; younger siblings (matched pairs of siblings )
    (b) before; after
    (c) sample from FA; sample from FB ( both randomly chosen)
    (d) age of patients: older sample;  younger sample (both selected at random)
    
2. Which of the above are independent samples:                            

3. A study is done of accidents comparing two cities by sampling and finding the mean number of accidents per day.  State the Null Hypothesis.                                    

4. Calculate the standard error if two samples sizes n1=25, n2=19, and standard deviations of the samples were s1= 3.1, s2=4.2.                                            

5. Calculate the correct test statistic for the following scenarios:                     
    a)  
    b)   
    c)   

6. Find the critical values for the F distribution for the following:
    a)                                   
    b)   
c)   

7. A pretest was given a group of students. Then they were given the opportunity to study an intensely interesting course in statistics.  Then they were given a post test. Their Marks were as follows:

    Fred    Wilma    Hi    Lois    Bert    Ernie    Mikey    Samantha
Pre test    10    48    1    50    11    1    15    36
Post test    02    01    11    81    64    79    16    36

Test the Conjecture that the Post test marks were higher than the pretest marks at a level of significance 0.05.
Organize your work according to the steps outlined in The Procedure for Hypothesis Testing. Marks will be given for each step.                                        

8. For the Post test marks in question 7, use the sign test to test the claim that the median is 65.