The SAT has gone through many revisions over the years. In 2005, a new writing s

Question

The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (Washington Post, August 30, 2006). Consider the scores on the writing component of the test of eight male and eight female students

Males

620

570

540

580

590

580

480

620

Females:

660

590

540

560

610

590

610

650

a. Constuct the null and the alternative hypothesis to test if females outscore males on writing tests

b. Assuming that the difference in scores is normally distributed, calculate the value of the test statistic. Do not assume that the population variances are equal.

c. Implement the test at a= 0.01 and interpret your results.

PLEASE EXAPLAIN HOW ANSWERES ARE FOUND, USING EXCEL

Explanation / Answer

Let u1 = mean of males
u2 = mean of females

a)

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

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b)

At level of significance =    0.01          
As we can see, this is a    left   tailed test.      
Calculating the means of each group, (using =AVERAGE() function)              
              
X1 =    572.5          
X2 =    601.25          
              
Calculating the standard deviations of each group (using =STDEV() function)              
              
s1 =    45.59135256          
s2 =    40.86126353          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    8          
n2 = sample size of group 2 =    8          
Thus, df = n1 + n2 - 2 =    14          
Also, sD =    21.64547957          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -1.3282219   [ANSWER, TEST STATISTIC]

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c)

Also, using p values, as this is one tailed,              
              
p =    0.102676062          

[ =TDIST(1.3282219, 14, 1) ]
              
As P > 0.01,    FAIL TO REJECT HO.

Hence, there is no significant evidence that females outscore males on writing tests. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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