document.write( "Question 1197158: An extract of a study conducted about the effects of a special class designed to aid students with
\n" ); document.write( "verbal skills is given below:
\n" ); document.write( "Each child was given a verbal skill test twice, both before and after completing a 4-week period
\n" ); document.write( "in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population
\n" ); document.write( "mean µ for Y is equal to 0, the class has no effect, on the average. For the four children in the
\n" ); document.write( "study, the observed values of Y are 8-5=3, 10-3=7, 5-2=3, and 7-4=3 (e.g. for the first child, the
\n" ); document.write( "scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5=3). It is planned to test the null hypothesis
\n" ); document.write( "of no effect against the alternative hypothesis that the effect is positive, based on the following
\n" ); document.write( "results from a statistical software package:
\n" ); document.write( "Variable Number of cases Mean Standard Deviation Standard Error
\n" ); document.write( "Y 4 4.000 2.000 1.000
\n" ); document.write( "1.1.1 Set up the null and alternative hypotheses. (4) \n" ); document.write( "
Algebra.Com's Answer #830292 by ewatrrr(24785)\"\" \"About 
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document.write( " Let Y = score on exam at time 2 - score on exam at time 1.\r\n" );
document.write( "  Y = {3,7,3,3}   µ = 4 and σ = 2    SE = 1\r\n" );
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document.write( "Ho: Y = 0    |  Ho must include =, ≤ , 0r  ≥ \r\n" );
document.write( "Ha: Y > 0  Claim\r\n" );
document.write( "'one-sided' \r\n" );
document.write( " \"t+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29\"\r\n" );
document.write( "  \"t+=blue+%280+-+4%29%2Fblue%282%2Fsqrt%284%29%29\"  = -4   \r\n" );
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document.write( "At 95% Confidence Level, critical value = 3.122 | =CONFIDENCE(alpha,standard_dev,size) = =CONFIDENCE(.05,2,4) = 3.182\r\n" );
document.write( "If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis.\r\n" );
document.write( "|-4| > 3.122 Reject Ho\r\n" );
document.write( "The test results support the claim that the Special class had a positive effect\r\n" );
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document.write( "Wish You the Best in your Studies.\r\n" );
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