Statistics and Probability V4 | Complete Solution

    Practice the following problems by hand just to see if you can get the numbers right. Using the following information, calculate the t-test statistic.

    ¯X_1  = 62         ¯X_2  = 60          n_1  = 10         n_2  = 10        s_1^2= 2.45            s_2^2= 3.16 
    ¯X_1  = 158       ¯X_2  = 157.4     n_1  = 22        n_2  = 26        s_1^2= 2.06           s_2^2= 2.59 
    ¯X_1  = 200       ¯X_2  = 198        n_1  = 17        n_2  = 17        s_1^2= 2.45           s_2^2= 2.35 

    Using the results you got from Question 1 and a level of significance at .05, what are the two-tailed critical values associated with each? Would the null hypothesis be rejected?

    In the following examples, indicate whether you would perform a t-test of independent means or dependent means.

    Two groups were exposed to different treatment levels for ankle sprains. Which treatment was most effective? 
    A researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas when others received the standard amount. 
    A group of adolescent boys was offered interpersonal skills counseling and then tested in September and May to see if there was any impact on family harmony. 
    One group of adult men was given instructions in reducing their high blood pressure whereas another was not given any instructions. 
    One group of men was provided access to an exercise program and tested two times over a 6-month period for heart health. 

    Complete by hand. A famous brand-name manufacturer wants to know whether people prefer Nibbles or Wribbles. They sample each type of cracker and indicate their like or dislike on a scale from 1 to 10. Which do they like the most? Paste your t-test output into your answer and write a very brief analysis.

Nibbles rating    Wribbles rating
9    4
3    7
1    6
6    8
5    7
7    7
8    8
3    6
10    7
3    8
5    9
2    8
9    7
6    3
2    6
5    7
8    6
1    5
6    5
3    6

    Using the following table, provide three examples of a simple one-way ANOVA, two examples of a two-factor ANOVA, and one example of a three-factor ANOVA. Complete the table for the missing examples. Identify the grouping and the test variable.

Design    Grouping variable(s)    Test variable
Simple ANOVA    Four levels of hours of training—2, 4, 6, and 8 hours    Typing accuracy
    Enter Your Example Here    Enter Your Example Here
    Enter Your Example Here    Enter Your Example Here
    Enter Your Example Here    Enter Your Example Here
Two-factor ANOVA    Two levels of training and gender (two-way design)    Typing accuracy
    Enter Your Example Here    Enter Your Example Here
    Enter Your Example Here    Enter Your Example Here
Three-factor ANOVA    Two levels of training, two of gender, and three of income    Voting attitudes
    Enter Your Example Here    Enter Your Example Here

    When would you use a factorial ANOVA rather than a simple ANOVA to test the significance of the difference between the averages of two or more groups?

    Create a drawing or plan for a 2 × 3 experimental design that would lend itself to a factorial ANOVA. Identify the independent and dependent variables. 

Complete the questions below. Be specific and provide examples when relevant. 

Question    Answer
What is meant by independent samples? Provide a research example of two independent samples.    
When is it appropriate to use a t-test for dependent samples? What is the key piece of information you must know in order to decide?    
When is it appropriate to use an ANOVA? What is the key piece of information you must know in order to decide?    
Why would you want to do an ANOVA when you have more than two groups, rather than just comparing each pair of means with a t-test?