5.20 High School and Beyond, PartI: The National Center of Education Statistics

Question

5.20 High School and Beyond, PartI: The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. USE YOUR TI CALCULATOR. 80 60 40 20 read write 40 30 20 10 10 10 20 Differences in scores (read - write) (a) Are the reading and writing scores of each student independent of each other? yes, because reading and writing are two different activities no, they are paired since each student has both a reading score and a writing score yes, they are independent because reading and writing have different means (b) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? Ho: Hdiff Ho: Haiff_0 Ho: Hdiff 0 Ha: Hdiff

Explanation / Answer

a)

OPTION B: No, they are paired since each student has both a reading score and a writing score.

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b)

"Is there evident difference", so it is two tailed:

OPTION A: Ho: udiff = 0, Ha: udiff =/= 0. [ANSWER]

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c)

  
              
              
Getting the test statistic, as              
              
X = sample mean =    -0.545          
uo = hypothesized mean =    0          
n = sample size =    200          
s = standard deviation =    8.887          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.867273986 [ANSWER, TEST STATISTIC]          
              
Also, the p value is              
              
p =    0.385791907   [ANSWER, P VALUE]      
              
As P is large (P > 0.05), we fail to reject Ho.

Hence.

OPTION B: Since p > alpha, we do not have enough evidence to reject the null hypothesis. [ANSWER]

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d)

OPTION C: Yes, because the evidence was not strong enough to suggest that the average readig and writing scores differ. [ANSWER]  

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