document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077021>Question 1077021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a&#8203; survey, <BR>\n" );
document.write( "39&#8203;% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too&#8203; high, so <BR>\n" );
document.write( " randomly selected 150 pet owners and discovered that <BR>\n" );
document.write( "54 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have a right to be&#8203; skeptical? Use the &#945;=0.1 level of significance.\r<BR>\n" );
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document.write( "I'm having trouble finding the P value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691585 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let p = population proportion of people who talk to their pets  on the answering machine or telephone. The initial survey claims that p = 0.39, so the null hypothesis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B0%5D%3A+p+=+0.39 ALIGN=MIDDLE  ALT=\"H%5B0%5D%3A+p+=+0.39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In contrast, the alternative hypothesis is where the veterinarian is making the claim that the value of p is too high. Therefore, the veterinarian believes p should be lower than 0.39, so the alternative hypothesis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B1%5D%3A+p+%3C+0.39 ALIGN=MIDDLE  ALT=\"H%5B1%5D%3A+p+%3C+0.39\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means we have a <font color = blue>left tailed test</font>. This fact is important to figure out the p value.\r<BR>\n" );
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document.write( "Summarizing things so far, we know\r<BR>\n" );
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document.write( "Null Hypothesis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B0%5D%3A+p+=+0.39 ALIGN=MIDDLE  ALT=\"H%5B0%5D%3A+p+=+0.39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Alternative Hypothesis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B1%5D%3A+p+%3C+0.39 ALIGN=MIDDLE  ALT=\"H%5B1%5D%3A+p+%3C+0.39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a <font color = blue>left tailed test</font>\r<BR>\n" );
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document.write( "Next we need to find the test statistic. Use the formula below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28phat+-+p%29%2F%28SE%29 ALIGN=MIDDLE  ALT=\"z+=+%28phat+-+p%29%2F%28SE%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=phat ALIGN=MIDDLE  ALT=\"phat\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sample proportion = x/n = 54/150 = 0.36<BR>\n" );
document.write( "p = hypothesized population proportion<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%28p%2A%281-p%29%2Fn%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%28p%2A%281-p%29%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's calculate the standard error (SE) first. Plug in p = 0.39 and the sample size n = 150 to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%28p%2A%281-p%29%2Fn%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%28p%2A%281-p%29%2Fn%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=SE+=+sqrt%280.39%2A%281-0.39%29%2F150%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%280.39%2A%281-0.39%29%2F150%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=SE+=+0.03982461550348 ALIGN=MIDDLE  ALT=\"SE+=+0.03982461550348\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which then tells us that...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28phat+-+p%29%2F%28SE%29 ALIGN=MIDDLE  ALT=\"z+=+%28phat+-+p%29%2F%28SE%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=z+=+%280.36+-+0.39%29%2F%280.03982461550348%29 ALIGN=MIDDLE  ALT=\"z+=+%280.36+-+0.39%29%2F%280.03982461550348%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=z+=+-0.75330294142773 ALIGN=MIDDLE  ALT=\"z+=+-0.75330294142773\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The test statistic is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-0.75330294142773 ALIGN=MIDDLE  ALT=\"z+=+-0.75330294142773\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The p value is going to be equal to the area under the standard normal curve to the <font color = blue>left</font> of this test statistic. \r<BR>\n" );
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document.write( "We can use a table or a calculator to find this approximate area. I recommend using <a  rel=nofollow HREF= \"https://www.wolframalpha.com/input/?i=normalcdf(-99,+-0.75330294142773)\">calculator</a> which reports approximately 0.2256\r<BR>\n" );
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document.write( "The p value is approximately <font color=red>0.2256</font>\r<BR>\n" );
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document.write( "Since the p value is larger than alpha = 0.1, this means that we fail to reject the null. We must accept that p = 0.39. We don't have enough evidence to overturn it.  </SPAN>\n" );
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