A nonprofit company concerned with the school dropout rates has designed a tutor

Question

A nonprofit company concerned with the school dropout rates has designed a tutoring program aimed at students between 16 to 18 years old. A national center for educational statistics reported that the high school dropout rate for the year 2000 was 11.8%. One school district, who adopted the use of the nonprofit's tutoring program and whose dropout rate has always been very close to the national average, reported in 2004 that 173 of their 1783 students dropped out. Is their experience evidence that the tutoring program has been effective? Determine the hypotheses for this test. Choose the correct answer below. A. H_0: p notequalto 0.118 H_A: p = 0.188 B. H_0: p = 0.118 H_A: p = 0.118 C. H_0: p = 0.118 H_A: p notequalto 0.118 D. H_0: p = 0.118 H_A L p 0.118 E. H_0: p lessthanorequalto 0.118 H_A: p = 0.118 F. H_0: P = 0.118 H_A: p

Explanation / Answer

(a) Ho: p = 0.118 versus Ha: p < 0.118

(b)

Data:      

n = 1783     

p = 0.118     

p' = 173/1783 = 0.097027     

Hypotheses:     

Ho: p = 0.118     

Ha: p < 0.118     

Decision Rule:     

= 0.05     

Critical z- score = -1.6449    

Reject Ho if z < -1.6449    

Test Statistic:     

SE = {p (1 - p)/n} = (0.118 * (1 - 0.118)/1783) = 0.0076   

z = (p' - p)/SE =   (0.0970274817722939 - 0.118)/0.0076401102316796 =    -2.75

(c) p- value = 0.0030     

Decision (in terms of the hypotheses):    

Since -2.7451 < -1.6449 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the dropout rate is now lower.

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