document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202805>Question 1202805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.883 g and a standard deviation of 0.289 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 33 cigarettes with a mean nicotine amount of 0.777 g.\r<BR>\n" );
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document.write( "Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 33 cigarettes with a mean of 0.777 g or less.<BR>\n" );
document.write( "P(M < 0.777 g) = \r<BR>\n" );
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document.write( "Enter your answer as a number accurate to 4 decimal places.\r<BR>\n" );
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document.write( "Based on the result above, is it valid to claim that the amount of nicotine is lower?\r<BR>\n" );
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document.write( "No. The probability of obtaining this data is high enough to have been a chance occurrence.<BR>\n" );
document.write( "Yes. The probability of this data is unlikely to have occurred by chance alone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837925 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean = .883<BR>\n" );
document.write( "population standard deviation  = .289<BR>\n" );
document.write( "sample size = 33<BR>\n" );
document.write( "sample mean = .777<BR>\n" );
document.write( "you want to find the probability of getting an amount of nicotine less than .777 from this sample.<BR>\n" );
document.write( "z-score formula is z = (x-m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "standard error = population standard deviation divied by square root of sample size = .289 / sqrt(33) = .0503.<BR>\n" );
document.write( "z-score formula becomes z = (.777 - .883) / .0503 = -2.1074.<BR>\n" );
document.write( "the probability of getting a z-score less than that is equal to .0275.<BR>\n" );
document.write( "that's a pretty low probability.<BR>\n" );
document.write( "if you were tyesting at .05 one tail level of significance, the results would be considered significant and you would conclude that the probability of getting a z-score this low is leess likely to be due to random variations in the mean of a sample of this size and more likely that the actual meana really is lower.<BR>\n" );
document.write( "if you were testing at .01 one tail level of significance, the resuls would be considered not significant and you would conclude that the proability of getting a z-sore this low is more likely to be due to random variations in the mean of a sample of this size and so you would considered the assumed population mean to be valid.<BR>\n" );
document.write( "i ran this through a one sample z-test calculator and it came up with the same conclusion.<BR>\n" );
document.write( "here are the results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/061811.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/061812.jpg\">\r<BR>\n" );
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document.write( "the first is significant at .05 level of significance.<BR>\n" );
document.write( "the second is not significance at .01 level of significance.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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