Show all your work for credit Solve the problemsl3 by answer

Show all your work for credit Solve the problems(l-3) by answering State the claim, H0, H1, Test statistic, Critical value(s), Conclusion and final statement Good luck. The mean ACT score for 43 male high school students is 21.2 and the standard deviation is 4.9. The mean ACT score for 56 female High School students is 20.9 and the standard deviation is 4.6. At a - 0.01, do male and female high school students have equal ACT scores?

Solution

a)

Male and female high school students have equal mean ACT scores. [ANSWER]

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b)

Let

u1 = mean of male
u2 = mean of female

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [ANSWER]

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c)

At level of significance =    0.01          
A
s we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    21.2          
X2 =    20.9          
              
Calculating the standard deviations of each group,              
              
s1 =    4.9          
s2 =    4.6          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    43          
n2 = sample size of group 2 =    56          

Thus,

sD =    0.967589394          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    0.310048872   [ANSWER]

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d)      
              
where uD = hypothesized difference =    0          
              
Now, the critical value for z is              
              
zcrit =    +/-   2.576   [ANSWER]

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e)  
              
As |z| < 2.576,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence taht the mean scores of female and male high school students in ACT are different at 0.01 level. [CONCLUSION]