document.write( "Question 1203076: The average math score for the class 6 is 23.6. A researcher is interested to check if the score is higher in class 6 that in the USA. How many students are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in score of 2 marks? If the population standard deviation is 5.7. \n" ); document.write( "
Algebra.Com's Answer #838470 by Jason57t(3)\"\" \"About 
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To find the sample size required for a statistical hypothesis test with a certain power, we use the formula for the sample size in a two-sided hypothesis test:\r
\n" ); document.write( "\n" ); document.write( "n = [(Zα/2 + Zβ)^2 * (2 * σ^2)] / d^2\r
\n" ); document.write( "\n" ); document.write( "Where:\r
\n" ); document.write( "\n" ); document.write( "Zα/2 is the critical value of the Normal distribution at α/2 (for a two-sided test with a significance level of 0.05, the value of Zα/2 is 1.96)
\n" ); document.write( "Zβ is the critical value of the Normal distribution at β (for a test with a power of 0.80, β is 0.20, and the value of Zβ is 0.84)
\n" ); document.write( "σ is the standard deviation of the population (in your case, σ = 5.7)
\n" ); document.write( "d is the size of the effect you're looking for (in your case, the difference in scores, d = 2)
\n" ); document.write( "Plugging these values into the formula:\r
\n" ); document.write( "\n" ); document.write( "n = [(1.96 + 0.84)^2 * (2 * 5.7^2)] / 2^2
\n" ); document.write( "n = [(2.8)^2 * (2 * 32.49)] / 4
\n" ); document.write( "n = [7.84 * 64.98] / 4
\n" ); document.write( "n = 509.9152 / 4
\n" ); document.write( "n = 127.4788\r
\n" ); document.write( "\n" ); document.write( "Because you can't have a fraction of a student, you'd round up to the nearest whole number. Therefore, the researcher would need a sample size of 128 students to ensure that the two-sided test of hypothesis has 80% power to detect a difference in scores of 2 marks. \n" ); document.write( "
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