document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181285>Question 1181285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A recent gasoline survey said that the national average price of gasoline was $1.498 a gallon It was felt that gasoline in Texas was significantly lower than the national averageA survey of 10 different suburbs in Dallas , Texas found the average price of gasoline to be a gallon with a standard deviation of $0.326. Find the p-value for this 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 #850063 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</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=850063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the p-value for this hypothesis test:\r<BR>\n" );
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document.write( "**1. State the Hypotheses:**\r<BR>\n" );
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document.write( "*   Null Hypothesis (H0): The average price of gasoline in Texas is the same as the national average (μ = $1.498).<BR>\n" );
document.write( "*   Alternative Hypothesis (H1): The average price of gasoline in Texas is significantly lower than the national average (μ < $1.498). This is a left-tailed test.\r<BR>\n" );
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document.write( "**2. Significance Level:** While not explicitly stated, we'll proceed with a common significance level, such as α = 0.05, if needed for a conclusion later.\r<BR>\n" );
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document.write( "**3. Calculate the Test Statistic (t-score):**\r<BR>\n" );
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document.write( "Since the sample size is small (n = 10) and the population standard deviation is unknown, we use a t-test.\r<BR>\n" );
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document.write( "t = (sample mean - population mean) / (sample standard deviation / √sample size)\r<BR>\n" );
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document.write( "t = (1.25 - 1.498) / (0.326 / √10)<BR>\n" );
document.write( "t = -0.248 / (0.326 / 3.162)<BR>\n" );
document.write( "t ≈ -0.248 / 0.103<BR>\n" );
document.write( "t ≈ -2.41\r<BR>\n" );
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document.write( "**4. Determine the Degrees of Freedom:**\r<BR>\n" );
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document.write( "Degrees of freedom (df) = n - 1 = 10 - 1 = 9\r<BR>\n" );
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document.write( "**5. Find the P-value:**\r<BR>\n" );
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document.write( "Because this is a left-tailed test, the p-value is the probability of getting a t-score as extreme as -2.41 or *lower*. Use a t-table or a statistical calculator to find this probability.\r<BR>\n" );
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document.write( "For a t-score of -2.41 and 9 degrees of freedom, the p-value is approximately 0.018.\r<BR>\n" );
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document.write( "**6. Conclusion (if α = 0.05):**\r<BR>\n" );
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document.write( "Since the p-value (0.018) is *less than* the significance level (0.05), we *reject* the null hypothesis.\r<BR>\n" );
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document.write( "**7. Conclusion Statement:**\r<BR>\n" );
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document.write( "There is sufficient evidence at the 0.05 significance level to conclude that the average price of gasoline in Texas is significantly lower than the national average.<BR>\n" );
document.write( " </SPAN>\n" );
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