numerous studies have found that males 9. Chapter 10 Numerous studies have found

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numerous studies have found that males

9. Chapter 10 Numerous studies have found that males report higher self-esteem than fermales, especially for adolescents (Klrg Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of M-39.0 with SS-60.2 for a sample or n-10 male adolescents and a mean cf M-35.4 with SS-69.4 for a sample of n-10 female adclescents Do the results indicate that self-esteem is significantly higher for males? Use ore tailed test with ,01. O Reject the null hypothesis. There is a significant difference between the two groups. O Reject the nul hypothesis. There is a no significant diffearence between the two groups. O Fail to reject the null hypothesis. There is a significant dfference beween the two groups Use the data to make a 955t confidence nterval estimate of the mean difference in self-esteem between male and female adolescents O 2.079 to 6.121 points lower for boys O 1.079 to 6.121 points higher for boys 2.079 to 5.121 points higher for boys Write a sentence domonstrating how the resuts from the hyoothesis test and the confidence interval would appear in a research report.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.01          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    39          
X2 =    35.4          
              
Calculating the standard deviations of each group,              
              
s1 =    2.586288632          
s2 =    2.776888747          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    18          
Also, sD =    1.2          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    3          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =        2.55237963      
              
      
              
Also, using p values, as this is right tailed,          
              
p =    0.003842706          
              
As t > 2.552, and P < 0.01,   WE REJECT THE NULL HYPOTHESIS.          
              
[ANSWER: OPTION A]              
              
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b)      
              
For the   0.95   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    2.10092204          

Thus,
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    1.078893552          
upper bound = [X1 - X2] + t(alpha/2) * sD =    6.121106448          
              
Thus, the confidence interval is              
              
(   1.078893552   ,   6.121106448   ) [OPTION B, ANSWER]

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c)

The results indicate that adolescent males have significantly higher self-esteem than girls, with the difference between 1.079 to 6.121 at 95% confidence, and with P value of 0.0038. [ANSWER]

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