document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165133>Question 1165133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.<BR>\n" );
document.write( "3.7	2.9	3.8	4.2	4.8	3.1<BR>\n" );
document.write( "The sample mean is x bar = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use α = 0.10.\r<BR>\n" );
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document.write( "Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)\r<BR>\n" );
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document.write( "(c) Find (or estimate) the P-value.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789590 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming all the randomness, normality, etc.<BR>\n" );
document.write( "z=(x bar-mean)/s/sqrt(6)<BR>\n" );
document.write( "=(3.75-4.30)*sqrt(6)/0.64<BR>\n" );
document.write( "=-2.105 or -2.11<BR>\n" );
document.write( "one way test p-value is 0.017\r<BR>\n" );
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document.write( "The data suggest that the mean weight of these birds is < 4.30 gm.\r<BR>\n" );
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