document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180574>Question 1180574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the null hypothesis and the alternative hypothesis in (a) words and in <BR>\n" );
document.write( "(b) symbols for each of the following. <BR>\n" );
document.write( "a. A librarian of a school claims that all their grade 8 students read an <BR>\n" );
document.write( "average of 10 storybooks a month with a standard deviation of 2 books. <BR>\n" );
document.write( "A random sample of grade 8 students read an average 12 books a month <BR>\n" );
document.write( "and a standard deviation of 1 book. The confidence statement is 95%. <BR>\n" );
document.write( "b. According to a factory employer, the mean working time of workers in <BR>\n" );
document.write( "the factory is 6 hours with a standard deviation of 0.5 hours. A <BR>\n" );
document.write( "researcher interviewed 50% of the employees and found out that their <BR>\n" );
document.write( "mean working time is 8 hours with a standard deviation of 1 hour. The a <BR>\n" );
document.write( "level is 0.05. <BR>\n" );
document.write( "Sketch the graph of each null and alternative hypothesis (one-tailed test and two-tailed test) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850104 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=850104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the breakdown of null and alternative hypotheses, both in words and symbols, along with sketches of their graphs:\r<BR>\n" );
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document.write( "**a. Librarian's Claim:**\r<BR>\n" );
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document.write( "The librarian claims the average number of storybooks read by Grade 8 students is 10. The sample shows an average of 12.  We'll consider both one-tailed (right-tailed) and two-tailed tests.\r<BR>\n" );
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document.write( "**(a) Hypotheses:**\r<BR>\n" );
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document.write( "**One-Tailed (Right-Tailed):**\r<BR>\n" );
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document.write( "*   **H0 (Words):** The average number of storybooks read by Grade 8 students is equal to 10.<BR>\n" );
document.write( "*   **H1 (Words):** The average number of storybooks read by Grade 8 students is greater than 10.<BR>\n" );
document.write( "*   **H0 (Symbols):** μ = 10<BR>\n" );
document.write( "*   **H1 (Symbols):** μ > 10\r<BR>\n" );
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document.write( "**Two-Tailed:**\r<BR>\n" );
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document.write( "*   **H0 (Words):** The average number of storybooks read by Grade 8 students is equal to 10.<BR>\n" );
document.write( "*   **H1 (Words):** The average number of storybooks read by Grade 8 students is *not* equal to 10.<BR>\n" );
document.write( "*   **H0 (Symbols):** μ = 10<BR>\n" );
document.write( "*   **H1 (Symbols):** μ ≠ 10\r<BR>\n" );
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document.write( "**(b) Graphs:**\r<BR>\n" );
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document.write( "**One-Tailed (Right-Tailed):**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "        H0: μ = 10                     H1: μ > 10<BR>\n" );
document.write( "    ---------------------           ---------------------<BR>\n" );
document.write( "   |                     |           |        /          |<BR>\n" );
document.write( "   |                     |           |       /           |<BR>\n" );
document.write( "   |        /            |           |      /            |<BR>\n" );
document.write( "   |       /             |           |     /             |<BR>\n" );
document.write( "   |      /              |           |    /              |<BR>\n" );
document.write( "   |     /               |           |   /               |<BR>\n" );
document.write( "   |    /                |           |  /                |<BR>\n" );
document.write( "   |   /                 |           | /                 |<BR>\n" );
document.write( "   |  /                  |           |/                  |<BR>\n" );
document.write( "   ---------------------           ---------------------<BR>\n" );
document.write( "      10                  x̄             10                 x̄<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Two-Tailed:**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "        H0: μ = 10                     H1: μ ≠ 10<BR>\n" );
document.write( "    ---------------------           ---------------------<BR>\n" );
document.write( "   |        /          |           |      / \          |<BR>\n" );
document.write( "   |       /           |           |     /   \         |<BR>\n" );
document.write( "   |      /            |           |    /     \        |<BR>\n" );
document.write( "   |     /             |           |   /       \       |<BR>\n" );
document.write( "   |    /              |           |  /         \      |<BR>\n" );
document.write( "   |   /               |           | /           \     |<BR>\n" );
document.write( "   |  /                |           |/             \    |<BR>\n" );
document.write( "   | /                 |           |               \   |<BR>\n" );
document.write( "   |/                  |           |                 \  |<BR>\n" );
document.write( "   ---------------------           ---------------------<BR>\n" );
document.write( "      10                  x̄             10                 x̄<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**b. Factory Employer's Claim:**\r<BR>\n" );
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document.write( "The employer claims the mean working time is 6 hours. The researcher found a mean of 8 hours. We'll consider both one-tailed (right-tailed) and two-tailed tests.\r<BR>\n" );
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document.write( "**(a) Hypotheses:**\r<BR>\n" );
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document.write( "**One-Tailed (Right-Tailed):**\r<BR>\n" );
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document.write( "*   **H0 (Words):** The mean working time is equal to 6 hours.<BR>\n" );
document.write( "*   **H1 (Words):** The mean working time is greater than 6 hours.<BR>\n" );
document.write( "*   **H0 (Symbols):** μ = 6<BR>\n" );
document.write( "*   **H1 (Symbols):** μ > 6\r<BR>\n" );
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document.write( "**Two-Tailed:**\r<BR>\n" );
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document.write( "*   **H0 (Words):** The mean working time is equal to 6 hours.<BR>\n" );
document.write( "*   **H1 (Words):** The mean working time is *not* equal to 6 hours.<BR>\n" );
document.write( "*   **H0 (Symbols):** μ = 6<BR>\n" );
document.write( "*   **H1 (Symbols):** μ ≠ 6\r<BR>\n" );
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document.write( "**(b) Graphs:**\r<BR>\n" );
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document.write( "**One-Tailed (Right-Tailed):**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "        H0: μ = 6                     H1: μ > 6<BR>\n" );
document.write( "    ---------------------           ---------------------<BR>\n" );
document.write( "   |                     |           |        /          |<BR>\n" );
document.write( "   |                     |           |       /           |<BR>\n" );
document.write( "   |        /            |           |      /            |<BR>\n" );
document.write( "   |       /             |           |     /             |<BR>\n" );
document.write( "   |      /              |           |    /              |<BR>\n" );
document.write( "   |     /               |           |   /               |<BR>\n" );
document.write( "   |    /                |           |  /                |<BR>\n" );
document.write( "   |   /                 |           | /                 |<BR>\n" );
document.write( "   |  /                  |           |/                  |<BR>\n" );
document.write( "   ---------------------           ---------------------<BR>\n" );
document.write( "       6                  x̄              6                  x̄<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Two-Tailed:**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "        H0: μ = 6                     H1: μ ≠ 6<BR>\n" );
document.write( "    ---------------------           ---------------------<BR>\n" );
document.write( "   |        /          |           |      / \          |<BR>\n" );
document.write( "   |       /           |           |     /   \         |<BR>\n" );
document.write( "   |      /            |           |    /     \        |<BR>\n" );
document.write( "   |     /             |           |   /       \       |<BR>\n" );
document.write( "   |    /              |           |  /         \      |<BR>\n" );
document.write( "   |   /               |           | /           \     |<BR>\n" );
document.write( "   |  /                |           |/             \    |<BR>\n" );
document.write( "   | /                 |           |               \   |<BR>\n" );
document.write( "   |/                  |           |                 \  |<BR>\n" );
document.write( "   ---------------------           ---------------------<BR>\n" );
document.write( "       6                  x̄              6                  x̄<BR>\n" );
document.write( "```<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );