document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153956>Question 1153956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this information: the sampled population is normally distributed, X  -  = 36.5, σ = 3, and n = 20. <BR>\n" );
document.write( "a. What is the 95% confidence interval estimate for μ? <BR>\n" );
document.write( "b. Are the assumptions satisfied? Explain why.<BR>\n" );
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document.write( "a. What is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95 ALIGN=MIDDLE  ALT=\"95\"   DISABLED_style= \"max-width:90%; height:auto;\" >% confidence interval estimate for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95 ALIGN=MIDDLE  ALT=\"95\"   DISABLED_style= \"max-width:90%; height:auto;\" >% the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.96 ALIGN=MIDDLE  ALT=\"1.96\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this formula for the Confidence Interval\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" >-  ±  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z%28delta%2Fsqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"Z%28delta%2Fsqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" >-=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5+ ALIGN=MIDDLE  ALT=\"36.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the mean<BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z=1.96 ALIGN=MIDDLE  ALT=\"Z=1.96\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is the chosen <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" >-value from the table  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta=3 ALIGN=MIDDLE  ALT=\"delta=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the standard deviation<BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=20 ALIGN=MIDDLE  ALT=\"n=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is the number of observations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5 ALIGN=MIDDLE  ALT=\"36.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ±  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.96%283%2Fsqrt%2820%29%29 ALIGN=MIDDLE  ALT=\"1.96%283%2Fsqrt%2820%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5+ ALIGN=MIDDLE  ALT=\"36.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ±  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.96%280.67082%29 ALIGN=MIDDLE  ALT=\"1.96%280.67082%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5 ALIGN=MIDDLE  ALT=\"36.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ±  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.31 ALIGN=MIDDLE  ALT=\"1.31\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5++%2B++1.31=37.8 ALIGN=MIDDLE  ALT=\"36.5++%2B++1.31=37.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5++-+1.31=35.2 ALIGN=MIDDLE  ALT=\"36.5++-+1.31=35.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words: from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35.2 ALIGN=MIDDLE  ALT=\"35.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37.8 ALIGN=MIDDLE  ALT=\"37.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Are the assumptions satisfied? Explain why.\r<BR>\n" );
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document.write( "A common assumption across all inferential tests is that the observations in your sample are independent from each other, meaning that the measurements for each sample subject are in no way influenced by or related to the measurements of other subjects.\r<BR>\n" );
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document.write( "Typical assumptions are:\r<BR>\n" );
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document.write( "    Normality: Data have a normal distribution (or at least is symmetric)<BR>\n" );
document.write( "    Homogeneity of variances: Data from multiple groups have the same variance<BR>\n" );
document.write( "    Linearity: Data have a linear relationship<BR>\n" );
document.write( "    Independence: Data are independent\r<BR>\n" );
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document.write( "Therefore, your confidence interval applies to the sample mean, not the population mean. Ideally your data should be drawn from a normally distributed population. However, sample means of large numbers of observations tend to be distributed normally, whatever the underlying distribution.\r<BR>\n" );
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