document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162495>Question 1162495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. You are a quality control officer for a hair-dryer company. If the percentage of defective hair- dryers that you test is statistically greater than 5%, then you have to get rid of the batch. You collect a simple random sample of 157 hair dryers and find that 9 of them are defective. Conduct a hypothesis test with a 𝛼𝛼 =.05 level of significance to determine if greater than 5% of the hair dryers are defective. Write all non-calculation answers in complete sentences.<BR>\n" );
document.write( "a. Which test would you use and why?<BR>\n" );
document.write( "b. Write the null and alternative hypothesis in complete sentences. (Make sure you mark<BR>\n" );
document.write( "which is the null and which is the alternative.)<BR>\n" );
document.write( "c. Write the null and alternative hypothesis as symbols.<BR>\n" );
document.write( "d. State the requirements that have been met to run the test.<BR>\n" );
document.write( "e. What is the test statistic and the p-value? (Make sure you use the right notation.)<BR>\n" );
document.write( "f. Should you reject or fail to reject the null hypothesis?<BR>\n" );
document.write( "g. State the conclusion for the test.<BR>\n" );
document.write( "h. According to the results of your hypothesis test, should you get rid of the batch. Explain<BR>\n" );
document.write( "your reasoning based upon the hypothesis test </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786374 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=786374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a 1 sample proportion test because you are testing a proportion greater or less than 5%<BR>\n" );
document.write( "Ho: the true proportion is <=5%<BR>\n" );
document.write( "Ha: the  proportion is> 5%<BR>\n" );
document.write( "alpha is 0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test statistic is a z<BR>\n" );
document.write( "reject if z >1.645<BR>\n" );
document.write( "SRS was done, and np and n(1-p) are both >5<BR>\n" );
document.write( "z=(p hat -0.05)/sqrt(p(1-p)/n)<BR>\n" );
document.write( "p hat=0.0573<BR>\n" );
document.write( "z=0.0073/0.0173<BR>\n" );
document.write( "z=0.42<BR>\n" );
document.write( "p-value is 0.34<BR>\n" );
document.write( "fail to reject Ho, since z < the critical value of 1.645<BR>\n" );
document.write( "There is insufficient evidence based on this sample to conclusively state at the 5% interval that the batch is defective.  If the true proportion were 5% we would have a 34% chance of having a result this much or more from the mean.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );