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After taking your Freshman English class, you notice there is quite a difference between the students in the classes related to your Business major and your general education requirements. You believe it comes down to a difference in verbal and math abilities. You are interested in seeing how your English classmates performed on two parts of the SAT. You randomly collect data from 28 students on their Math SAT score (population
1), and randomly select another 25 students and collect data on their Verbal SAT score (population
2). After entering the data into Excel you obtain the following output: t-Test: Two-Sample Assuming Unequal Variances Q=0.05 Math SAT Verbal SAT Mean 668. 7604 701.888 Variance 3826.406 6944.827 Observations 28 25 Hypothesized Mean Difference 0 df 44 t Stat P(T<=t) one-tail t Critical one-tail 1.68 P(T<=t) two-tail t Critical two-tail 2.01 What is the value of the test statistic to test if math and verbal scores differ in the SAT exam?
a. -1.479
b. There is not enough information to answer this question
C. -1.627
d. 30.116
e. 30.116

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is C

Step-by-step explanation:

From the question we are told that

  The sample  size for  Math SAT is  [tex]n_1 = 28[/tex]

   The  sample  size for  Verbal  SAT  is  [tex]n_2 = 25[/tex]

Generally the test statistics is mathematically represented as

 [tex]t = \frac{\mu_1 - \mu_2}{ \sqrt{\frac{\sigma^2_1 }{n_1} + \frac{\sigma_2^2}{n_2} } }[/tex]

substituting  668. 7604 for [tex] \mu_1[/tex] , 701.888 for [tex] \mu_2[/tex], 3826.406 for  [tex] \sigma_1^2[/tex] , 6944.827 for  [tex]\sigma_2^2[/tex]

So

     [tex]t = \frac{668.7604 - 701.888}{ \sqrt{\frac{3826.406}{28} + \frac{6944.827}{25} } }[/tex]  

=>   [tex]t =  1.627[/tex]

     

 

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