document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201153>Question 1201153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, please i need help solving this: The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies is the same. A Donaldson manager surveyed other employers in town to find what they paid the agencies for temporary secretaries. The results are summarized below. At alpha = 0.05, test the claim that each agency charges the same hourly wage.<BR>\n" );
document.write( "Agency A: x1 = 9.55/hr, $1 =$1.45/hr, n1= 20.<BR>\n" );
document.write( "Agency B: x1 = 9.25/hr, $1 =$1.25/hr, n1= 18.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848075 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><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=848075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Set up Hypotheses**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** μ1 - μ2 = 0 (The average hourly wage charged by both agencies is the same.)<BR>\n" );
document.write( "* **Alternative Hypothesis (Ha):** μ1 - μ2 ≠ 0 (The average hourly wage charged by both agencies is different.)\r<BR>\n" );
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document.write( "**2. Calculate the Pooled Variance**\r<BR>\n" );
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document.write( "* **Calculate the pooled variance (s²p):**<BR>\n" );
document.write( "   * s²p = [(n1 - 1) * s1² + (n2 - 1) * s2²] / (n1 + n2 - 2)<BR>\n" );
document.write( "   * s²p = [(20 - 1) * 1.45² + (18 - 1) * 1.25²] / (20 + 18 - 2)<BR>\n" );
document.write( "   * s²p = [48.025 + 26.25] / 36<BR>\n" );
document.write( "   * s²p = 2.064 \r<BR>\n" );
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document.write( "**3. Calculate the t-statistic**\r<BR>\n" );
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document.write( "* **t = (x̄1 - x̄2) / √[s²p * (1/n1 + 1/n2)]**<BR>\n" );
document.write( "* t = (9.55 - 9.25) / √[2.064 * (1/20 + 1/18)]<BR>\n" );
document.write( "* t = 0.3 / √[2.064 * (0.05 + 0.0556)]<BR>\n" );
document.write( "* t = 0.3 / √[2.064 * 0.1056]<BR>\n" );
document.write( "* t = 0.3 / √0.2179<BR>\n" );
document.write( "* t = 0.3 / 0.4668<BR>\n" );
document.write( "* t ≈ 0.642\r<BR>\n" );
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document.write( "**4. Determine Degrees of Freedom**\r<BR>\n" );
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document.write( "* Degrees of Freedom (df) = n1 + n2 - 2 = 20 + 18 - 2 = 36\r<BR>\n" );
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document.write( "**5. Find the Critical Value**\r<BR>\n" );
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document.write( "* Since this is a two-tailed test with α = 0.05 and df = 36, we find the critical values from the t-distribution table.<BR>\n" );
document.write( "* The critical values are approximately ±2.028.\r<BR>\n" );
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document.write( "**6. Make a Decision**\r<BR>\n" );
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document.write( "* Since the calculated t-value (0.642) falls within the critical region (±2.028), we **fail to reject the null hypothesis.**\r<BR>\n" );
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document.write( "**Conclusion:**\r<BR>\n" );
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document.write( "At the 0.05 level of significance, there is **not enough evidence** to conclude that the average hourly wages charged by the two employment agencies are different. \r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This analysis assumes that the populations of hourly wages for both agencies are normally distributed.<BR>\n" );
document.write( "* You can also use statistical software (like Excel or R) to perform the t-test and obtain the exact p-value.\r<BR>\n" );
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document.write( "I hope this helps! Let me know if you have any further questions.<BR>\n" );
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