document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133760>Question 133760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Can someone help me with these 2 questions, I'm a little confused as to what I am suppose to be doing.\r<BR>\n" );
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document.write( "1. You are the incoming inspector for potato chips – you are to ensure that each bag has 16 ounces or more in it.   You want your testing to be at the level of significance of 0.05. You pull a sample of 49 bags of chips from a recent truckload. Your sample statistics are:<BR>\n" );
document.write( "                    x-bar (the sample mean) =   15.9 ounces<BR>\n" );
document.write( "                    s ( the sample standard deviation) = 0.35 ounces<BR>\n" );
document.write( "(a)   what is the null and alternative hypothesis<BR>\n" );
document.write( "(b)   one or two tailed test ??  <BR>\n" );
document.write( "(c)   what is the critical z value for your test at the 0.05 level of significance?? <BR>\n" );
document.write( "(d)   what is the calculated z value ??<BR>\n" );
document.write( "(e)   what is your decision about the load of potato chips ??<BR>\n" );
document.write( "             -- reject ??     -- not-reject ??<BR>\n" );
document.write( "(a) Ho : &#956; <= 16   Vs    H1 : &#956; < 16 (Left tailed test)<BR>\n" );
document.write( "(b)	One tailed test<BR>\n" );
document.write( "(c)	Critical z = 1.645 <BR>\n" );
document.write( "(d)	Test Statistics:<BR>\n" );
document.write( "                 z =    follows N(0,1)<BR>\n" );
document.write( "            = -2<BR>\n" );
document.write( "where <BR>\n" );
document.write( "               x bar=15.9   n=49  s=0.35    &#956;= 16 <BR>\n" );
document.write( "(e)	Rejection Rule<BR>\n" );
document.write( "Critical Value = -1.645<BR>\n" );
document.write( "Thus we reject H0 if z < -1.645<BR>\n" );
document.write( "As z = -2 <  -1.645 we reject H0.<BR>\n" );
document.write( "At the 5% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude that each bag has less than 16 ounces.\r<BR>\n" );
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document.write( "2. An owner of a fast food restaurant reported to corporate headquarters that the average bill paid by his customers in the last quarter was $6.20 and that the standard deviation was $1.90. Not knowing exactly what the effect would be, headquarters suddenly launched a nationwide promotional campaign featuring a large quantity discount for a multi-sandwich purchase. The stubs from the next 81 purchases at the owner’s franchise after the campaign was launched averaged $6.65. <BR>\n" );
document.write( " <BR>\n" );
document.write( "Conduct the 5 step hypothesis test at a level of significance of 0.05 to determine if the promotion increased the average bill amount<BR>\n" );
document.write( "Ans.<BR>\n" );
document.write( "•	To Test <BR>\n" );
document.write( "            Ho : &#956;= 6.20  Vs    H1 : &#956; > 6.20 (Right tailed test)<BR>\n" );
document.write( "•	Level of significance = 0.05<BR>\n" );
document.write( "•	Test Statistics:<BR>\n" );
document.write( "                 z = xbar-&#956;/SE   follows N(0,1)<BR>\n" );
document.write( "            = 2.13<BR>\n" );
document.write( "where <BR>\n" );
document.write( "              xbar =6.65    n=81    sd=1.9    &#956;= 6.2   <BR>\n" );
document.write( "•	P-value = P(z > 2.13) = 0.0165<BR>\n" );
document.write( "              Since P-value of 0.0165 < 0.05 we reject H0. <BR>\n" );
document.write( "              It is statistically  significant <BR>\n" );
document.write( "•	Rejection Rule<BR>\n" );
document.write( "Critical Value = 1.645<BR>\n" );
document.write( "Thus we reject H0 if z > 1.645<BR>\n" );
document.write( "As z = 2.13 > 1.645 we reject H0.<BR>\n" );
document.write( "•	Conclusion<BR>\n" );
document.write( "At the 5% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude that the promotion increased the average bill amount.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97877 by </B><A HREF=/tutors/aboutme.mpl?userid=nanaktutors@yahoo.com><B>nanaktutors@yahoo.com(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nanaktutors@yahoo.com><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=97877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  1. You are the incoming inspector for potato chips – you are to ensure that each bag has 16 ounces or more in it.   You want your testing to be at the level of significance of 0.05. You pull a sample of 49 bags of chips from a recent truckload. Your sample statistics are:<BR>\n" );
document.write( "                    x-bar (the sample mean) =   15.9 ounces<BR>\n" );
document.write( "                    s ( the sample standard deviation) = 0.35 ounces<BR>\n" );
document.write( "(a)   what is the null and alternative hypothesis<BR>\n" );
document.write( "(b)   one or two tailed test ??  <BR>\n" );
document.write( "(c)   what is the critical z value for your test at the 0.05 level of significance?? <BR>\n" );
document.write( "(d)   what is the calculated z value ??<BR>\n" );
document.write( "(e)   what is your decision about the load of potato chips ??<BR>\n" );
document.write( "             -- reject ??     -- not-reject ??<BR>\n" );
document.write( "(a) Ho : &#956; <= 16   Vs    H1 : &#956; < 16 (Left tailed test)<BR>\n" );
document.write( "(b)	One tailed test<BR>\n" );
document.write( "(c)	Critical z = 1.645 <BR>\n" );
document.write( "(d)	Test Statistics:<BR>\n" );
document.write( "                 z =    follows N(0,1)<BR>\n" );
document.write( "            = -2<BR>\n" );
document.write( "where <BR>\n" );
document.write( "               x bar=15.9   n=49  s=0.35    &#956;= 16 <BR>\n" );
document.write( "(e)	Rejection Rule<BR>\n" );
document.write( "Critical Value = -1.645<BR>\n" );
document.write( "Thus we reject H0 if z < -1.645<BR>\n" );
document.write( "As z = -2 <  -1.645 we reject H0.<BR>\n" );
document.write( "At the 5% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude that each bag has less than 16 ounces.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. An owner of a fast food restaurant reported to corporate headquarters that the average bill paid by his customers in the last quarter was $6.20 and that the standard deviation was $1.90. Not knowing exactly what the effect would be, headquarters suddenly launched a nationwide promotional campaign featuring a large quantity discount for a multi-sandwich purchase. The stubs from the next 81 purchases at the owner’s franchise after the campaign was launched averaged $6.65. <BR>\n" );
document.write( " <BR>\n" );
document.write( "Conduct the 5 step hypothesis test at a level of significance of 0.05 to determine if the promotion increased the average bill amount<BR>\n" );
document.write( "Ans.<BR>\n" );
document.write( "•	To Test <BR>\n" );
document.write( "            Ho : &#956;= 6.20  Vs    H1 : &#956; > 6.20 (Right tailed test)<BR>\n" );
document.write( "•	Level of significance = 0.05<BR>\n" );
document.write( "•	Test Statistics:<BR>\n" );
document.write( "                 z = xbar-&#956;/SE   follows N(0,1)<BR>\n" );
document.write( "            = 2.13<BR>\n" );
document.write( "where <BR>\n" );
document.write( "              xbar =6.65    n=81    sd=1.9    &#956;= 6.2   <BR>\n" );
document.write( "•	P-value = P(z > 2.13) = 0.0165<BR>\n" );
document.write( "              Since P-value of 0.0165 < 0.05 we reject H0. <BR>\n" );
document.write( "              It is statistically  significant <BR>\n" );
document.write( "•	Rejection Rule<BR>\n" );
document.write( "Critical Value = 1.645<BR>\n" );
document.write( "Thus we reject H0 if z > 1.645<BR>\n" );
document.write( "As z = 2.13 > 1.645 we reject H0.<BR>\n" );
document.write( "•	Conclusion<BR>\n" );
document.write( "At the 5% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude that the promotion increased the average bill amount.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );