document.write( "Question 1203193: To conduct a hypothesis test of the claim that the population mean satisfaction rating of ABC employees is different from 3.2, you choose a random sample of 13 surveys. The sample has a mean satisfaction rating of 3.3 and a standard deviation of 0.6. If the sample is from a normally distributed population with an unknown standard deviation, choose an appropriate test statistic for your hypothesis test on the population mean. Then calculate that statistic. Round to two decimal. \n" ); document.write( "
Algebra.Com's Answer #838565 by Theo(13342)\"\" \"About 
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you would use the t-test because the standaard deviation is taken from the sample rather than from the population.
\n" ); document.write( "n = sample size = 13
\n" ); document.write( "pm = population mean = 3.2
\n" ); document.write( "sm = sample mean = 3.1
\n" ); document.write( "ssd = sample standard deviation = .6
\n" ); document.write( "sdof = sample degrees of freedom = sample size minus 1 = 12
\n" ); document.write( "se = standard error = ssd / sqrt(n) = sample standard deviation / square root of sample size = .6/sqrt(13) = .1664
\n" ); document.write( "t = (x - m) / s is your formula.
\n" ); document.write( "t = t-score
\n" ); document.write( "x = sample mean
\n" ); document.write( "m = population mean
\n" ); document.write( "s = standad error
\n" ); document.write( "formula becomes t = (3.1 - 3.2) / .1664 = -.60096
\n" ); document.write( "you would get the area to the left of that t-score with 12 degrees of freedom.
\n" ); document.write( "that's the test alpha which is equal to test p-value which is equal to .2795.
\n" ); document.write( "round to two decimal places to get .28.
\n" ); document.write( "that is compared to the critical p-value, which is usually .05 or .025 or .01.
\n" ); document.write( "the test results are considered significant if the test p-value is less than the critical p-value.
\n" ); document.write( "another test value would be the test t-score compare to the critical t-score.
\n" ); document.write( "your test t-score is equal to -.60096.
\n" ); document.write( "the critical t-score on the left side of the normal distribiution with 12 degrees of freedom is usually -1.78 at .05 critical alpha, or -2.18 at .025 critical slpha, or -2.68 at .01 critical alpha.
\n" ); document.write( "the test results are considered significant if the test t-score is greater than the critical t-score.
\n" ); document.write( "the two measures support each othr.
\n" ); document.write( "if the test t-score is greater than the critical t-score, then the test alpha is less than the critical alpha, and vice versa.
\n" ); document.write( "your test t-store is less than the critical t-score and your test alpha is greater than your critical alpha, both indications that the results are not significant.
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