Question

A researcher conducts a study to investigate any effect that watching the news has on one’s level of optimism. One group of participants are randomly assigned to watch a 60-minute recording of a local news episode and another group of participants are randomly assigned to watch a 60-minute biopic covering the life of a famous news anchor. The 11 people in the biopic condition averaged an optimism level of 72 (SD = 11) and the 16 people in the news condition averaged an optimism level of 61 (SD = 18).

1. Create a 99% confidence interval to estimate the difference in optimism when comparing those who participate in the local news condition versus those who participate in the biopic condition. Be sure to properly report your confidence interval in brackets. Also, be sure to show calculations properly per the instructions for credit.

2.. Using the confidence interval ONLY, was there a significant difference in optimism per what participants watched? Yes or No. Must explain/justify your answer for credit.

3. If you were to do a hypothesis test (using an alpha of .05), state the critical value you would use for the test. Also, briefly state how you arrived at that critical value.

4. Use the correct statistical analysis to compute the calculated test value. Be sure to show calculations properly per the instructions for credit.

5. Using the hypothesis test ONLY, was there a significant difference in optimism per what participants watched? Yes or No. Must explain/justify your answer for credit.

6. Regardless of your answer to the previous question, compute an effect size for this study. Be sure to show calculations properly per the instructions for credit.

7. Is that effect size considered small, medium, or large? Explain/justify your answer.

I know this is a lot, but I think just knowing what kind of a test I will need to do and knowing what the critical value would be is important as well.

Answer 1

2 MEAN T TEST FOR INDEPENDENT SAMPLES

1)

There is not enough evidence to                       
Degree of freedom, DF=   n1+n2-2 =    25              
t-critical value =    t α/2 =    2.7874   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    15.5820              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    6.1031              
margin of error, E = t*SE =    2.7874   *   6.1031   =   17.0120  
                      
difference of means =    x̅1-x̅2 =    61.0000   -   72.000   =   -11.0000
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    -11.0000   -   17.0120   =   -28.0120
Interval Upper Limit=   (x̅1-x̅2) + E =    -11.0000   +   17.0120   =   6.0120

CI (-28.012 , 6.012)

...................

2)

NO,

0 LIES WITHIN THE INTERVAL

SO, THERE IS NOT significant difference in optimism per what participants watched

..............

3)

2 TAIL TEST

Degree of freedom, DF=   n1+n2-2 =    25
t-critical value , t* = +- 2.0595

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4)

Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   61.00                  
standard deviation of sample 1,   s1 =    18.00                  
size of sample 1,    n1=   16                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   72.00                  
standard deviation of sample 2,   s2 =    11.00                  
size of sample 2,    n2=   11                  
                          
difference in sample means =    x̅1-x̅2 =    61.0000   -   72.0   =   -11.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    15.5820                  
std error , SE =    Sp*√(1/n1+1/n2) =    6.1031                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -11.0000   -   0   ) /    6.10   =   -1.802

........

5)

NO

there IS NOT a significant difference in optimism per what participants watched

| t-stat | < | critical value |, so, Do not Reject Ho      
.................

effect size,      
cohen's d =    |( x̅1-x̅2 )/Sp | =    0.706
LARGE

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THANKS

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