document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208660>Question 1208660</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( ") a baker stated that the average number of loaves of bread sold daily is 3000 with a standerd deviation of 100. An employer wants to test the accuracy of this statement. A randome sample of 35 days showed the average daily sales were 3000. Test at the 5% level of significance if the bakery's statement can be accepted<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 #849186 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to perform a hypothesis test to determine if the bakery's statement can be accepted:\r<BR>\n" );
document.write( "\n" );
document.write( "**1. State the Hypotheses:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Null Hypothesis (H0):** μ = 3000 (The average number of loaves sold daily is 3000.)<BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** μ ≠ 3000 (The average number of loaves sold daily is *not* 3000.)  This is a two-tailed test.\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Determine the Level of Significance:**\r<BR>\n" );
document.write( "\n" );
document.write( "α = 0.05 (5%)\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Calculate the Test Statistic:**\r<BR>\n" );
document.write( "\n" );
document.write( "Since we have a sample size greater than 30, we can use a z-test. The formula for the z-score is:\r<BR>\n" );
document.write( "\n" );
document.write( "z = (x̄ - μ) / (σ / √n)\r<BR>\n" );
document.write( "\n" );
document.write( "Where:\r<BR>\n" );
document.write( "\n" );
document.write( "* x̄ = sample mean (3050)<BR>\n" );
document.write( "* μ = population mean (3000)<BR>\n" );
document.write( "* σ = population standard deviation (100)<BR>\n" );
document.write( "* n = sample size (35)\r<BR>\n" );
document.write( "\n" );
document.write( "z = (3050 - 3000) / (100 / √35)<BR>\n" );
document.write( "z = 50 / (100 / 5.916)<BR>\n" );
document.write( "z ≈ 2.96\r<BR>\n" );
document.write( "\n" );
document.write( "**4. Find the P-value:**\r<BR>\n" );
document.write( "\n" );
document.write( "Because this is a two-tailed test, we need to find the area in *both* tails of the standard normal distribution that is beyond our z-score of 2.96.\r<BR>\n" );
document.write( "\n" );
document.write( "Using a z-table or calculator:\r<BR>\n" );
document.write( "\n" );
document.write( "P(z > 2.96) ≈ 0.0015<BR>\n" );
document.write( "P(z < -2.96) ≈ 0.0015\r<BR>\n" );
document.write( "\n" );
document.write( "P-value = 2 * 0.0015 = 0.003\r<BR>\n" );
document.write( "\n" );
document.write( "**5. Make a Decision:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Compare the P-value to the significance level (α):\r<BR>\n" );
document.write( "\n" );
document.write( "Since the P-value (0.003) is *less than* the significance level (0.05), we *reject* the null hypothesis.\r<BR>\n" );
document.write( "\n" );
document.write( "**6. Conclusion:**\r<BR>\n" );
document.write( "\n" );
document.write( "There is sufficient evidence at the 5% level of significance to reject the bakery's statement that the average number of loaves of bread sold daily is 3000. The sample data suggests that the true average daily sales are different from 3000.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );