document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181349>Question 1181349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a study conducted, 48.9% of males aged 20 to 39 years consume the recommended daily requirement of calcium. After an aggressive marketing campaign, a separate survey was conducted and they found that 21 of 35 randomly selected males aged 20 to 39 of them consume the recommended daily requirement of calcium. At the α = 0.10 level of significance, is there evidence to conclude that the percentage of males aged 20 to 39 who consume the recommended daily requirement of calcium has increased?<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 #850058 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=850058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to conduct a hypothesis test to determine if the marketing campaign was effective:\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 percentage of males aged 20-39 who consume the recommended daily requirement of calcium has *not* increased. (p ≤ 0.489)<BR>\n" );
document.write( "*   **Alternative Hypothesis (H₁):** The percentage of males aged 20-39 who consume the recommended daily requirement of calcium *has* increased. (p > 0.489)  This is a right-tailed test.\r<BR>\n" );
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document.write( "**2. Determine the Level of Significance:**\r<BR>\n" );
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document.write( "α = 0.10\r<BR>\n" );
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document.write( "**3. Calculate the Sample Proportion (p̂):**\r<BR>\n" );
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document.write( "p̂ = (Number who consume recommended calcium) / (Total number surveyed)<BR>\n" );
document.write( "p̂ = 21 / 35<BR>\n" );
document.write( "p̂ = 0.6\r<BR>\n" );
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document.write( "**4. Calculate the Test Statistic (z-score):**\r<BR>\n" );
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document.write( "We use a z-test for proportions because the sample size is large enough.\r<BR>\n" );
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document.write( "z = (p̂ - p) / sqrt[p(1-p)/n]<BR>\n" );
document.write( "z = (0.6 - 0.489) / sqrt[(0.489 * 0.511) / 35]<BR>\n" );
document.write( "z = 0.111 / sqrt(0.00714)<BR>\n" );
document.write( "z = 0.111 / 0.0845<BR>\n" );
document.write( "z ≈ 1.31\r<BR>\n" );
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document.write( "**5. Determine the Critical Value (or P-value):**\r<BR>\n" );
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document.write( "*   **Critical Value Approach:** For a right-tailed test with α = 0.10, the critical z-value is approximately 1.28 (you can find this using a z-table or calculator).  If our calculated z-score is greater than 1.28, we reject the null hypothesis.\r<BR>\n" );
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document.write( "*   **P-value Approach:** The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.  Since this is a right-tailed test, we want the area to the *right* of our z-score (1.31) on the standard normal distribution. Using a z-table or calculator, we find that the p-value is approximately 0.095.\r<BR>\n" );
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document.write( "**6. Make a Decision:**\r<BR>\n" );
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document.write( "*   **Critical Value Approach:** Our calculated z-score (1.31) is *greater* than the critical value (1.28). Therefore, we *reject* the null hypothesis.\r<BR>\n" );
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document.write( "*   **P-value Approach:** Our p-value (0.095) is *less than* our significance level (0.10). Therefore, we *reject* the null hypothesis.\r<BR>\n" );
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document.write( "**7. State the Conclusion:**\r<BR>\n" );
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document.write( "There *is* sufficient evidence at the α = 0.10 level of significance to conclude that the percentage of males aged 20 to 39 who consume the recommended daily requirement of calcium has increased after the marketing campaign.<BR>\n" );
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