document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116576>Question 1116576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> home / study / math / statistics and probability / statistics and probability questions and answers / a distribution and the observed frequencies of the values of a variable from a simple random ...<BR>\n" );
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document.write( "Question: A distribution and the observed frequencies of the values of a variable from a simple random samp...<BR>\n" );
document.write( "A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided below. Use the? chi-square goodness-of-fit test to? decide, at the specified significance? level, whether the distribution of the variable differs from the given distribution.\r<BR>\n" );
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document.write( "Distribution: 0.2, 0.1, 0.1,0.2,0.4\r<BR>\n" );
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document.write( "Observed? frequencies: 14, 7, 44, 11,14\r<BR>\n" );
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document.write( "Significance level=0.10\r<BR>\n" );
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document.write( "i. Compute the value of the test statistic, chisquare\r<BR>\n" );
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document.write( "ii. Identify the P value\r<BR>\n" );
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document.write( "iii. Does the data provide sufficient evidence that the distribution of the variable differs from the given distribution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731464 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: The proportions are 0.2, 0.1, 0.1, 0.2, 0.4<BR>\n" );
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document.write( "H1: At least one of the proportions in Ho: is false<BR>\n" );
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document.write( "Degrees of Freedom(DF) = 5 - 1 = 4<BR>\n" );
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document.write( "The number of observations in the sample is 14 +7 +44 + 11 +14 = 90<BR>\n" );
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document.write( "The expected frequency counts are<BR>\n" );
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document.write( "E(1) = 0.2 * 90 = 18<BR>\n" );
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document.write( "E(2) = 0.1 * 90 = 9<BR>\n" );
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document.write( "E(3) = 0.1 * 90 = 9<BR>\n" );
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document.write( "E(4) = 0.2 * 90 = 18<BR>\n" );
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document.write( "E(5) = 0.4 * 90 = 36<BR>\n" );
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document.write( "chi^2 test statistic = summation i = 1, 5 of [((O(i) - E(i))^2/E(i)] where O(i) is the observed frequency count<BR>\n" );
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document.write( "chi^2(X) = ((14-18)^2/18) +((7-9)^2/9) ((44-9)^2/9) +((11-18)^2/18) +((14-36)^2/36) =  77.55<BR>\n" );
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document.write( "Use a Chi-Square Distribution Calculator to find P(X > 77.55) = 0<BR>\n" );
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document.write( "Since the P-value (0) is less than the significance level (0.10), we cannot accept the null hypothesis.<BR>\n" );
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