document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159163>Question 1159163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer claims that the mean lifetime of lithium batteries is more than 1400 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1580 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α = 0.05. Assume the distribution is normal. Use the Confidence Interval method. Exact value of the standard deviation is not known.  </SPAN>\n" );
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document.write( "Ho: Lifetime is 1400 hours <BR>\n" );
document.write( "Ha: Lifetime is not 1400 hours<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test is t0.975, df=24)<BR>\n" );
document.write( "critical value is t>2.064<BR>\n" );
document.write( "for 95%CI use mean+/-t*s/sqrt(n)<BR>\n" );
document.write( "this is 1580+/-2.064*80/sqrt(25)<BR>\n" );
document.write( "half-interval is 33 hours<BR>\n" );
document.write( "CI is (1547, 1613)<BR>\n" );
document.write( "1400 does not lie in the interval and therefore can assume the mean lifetime is not 1400 hours but rather longer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );