22 In the past 20 years or so sexual education in school has

22. In the past 20 years or so sexual education in school has either been eliminated or changed to \"abstinence only\" education, even though countless studies showed that \"abstinence only\" education programs have no effect on teen sexual activity or teen pregnancy. In recent years, there has been a switch back to programs that teach abstinence AND the use of condoms and contraceptives. Do the new programs have any effect on teen pregnancy? (Source (Links to an external site.))

The following data represent the number of teen pregnancies in a random sample of 6 different school districts in Harris County (Waco), Texas before and after the implementation of a comprehensive sexual education program focusing on abstinence AND the use of condoms and contraceptives. (Source (Links to an external site.)1 and Source2 (Links to an external site.), although numbers have been changed to protect the innocent. :) )

(No work needed here. Put a 0 in this box. Question to answer follows in 22.a.)

School District

Teen Pregnancies Before
the new Sex Ed Program (2008)

Teen Pregnancies After
the new Sex Ed Program (2011)

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Question 2612 ptsSkip to question text.

22. a. At the 0.01 level, can we say that the implementation of a comprehensive sexual education program has decreased teen pregnancies in Harris County (Waco), Texas? Show work as stated in the quiz directions.

You must type the following here - they must match what is on your work:
Test statistic, critical value or p-value, decision, and interpretation.

Solution

Let ud = u2 - u1.          
Formulating the null and alternative hypotheses,          
          
Ho:   ud   >=   0
Ha:   ud   <   0

At level of significance =    0.01      
As you can see, this is a    1   tailed test.  
          
Calculating the standard deviation of the differences (third column):          
          
s =    6.345602152      
          
Thus, the standard error of the difference is sD = s/sqrt(n):          
          
sD =    2.006655592      
          
Calculating the mean of the differences (third column):          
          
XD = -5.6      
          
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then  
          
t = -2.790713076   [TEST STATISTIC]

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As df = n - 1 =    5      
          
Then the critical value of t is          
          
tcrit = -3.364929999 [CRITICAL VALUE]

**********************************************      
          
Thus, comparing t and tcrit, we   WE FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Also, using p values,          
          
p =    0.019206253   [P VALUE]

**********************************************  
          
Also, comparing this p to the significance level,   WE FAIL TO REJECT THE NULL HYPOTHESIS.       [DECISION]
*********************************************

We have NO significant evidence that the implementation of a comprehensive sexual education program has decreased teen pregnancies in Harris County (Waco), Texas. [INTERPRETATION]