document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200633>Question 1200633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gaynor Advertising conducted a survey to determine individual’s main source of news as well as their educational level. 2500 individuals were surveyed and the results are given below:\r<BR>\n" );
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document.write( "Source of News Primary Secondary Graduate Post Graduate	Total<BR>\n" );
document.write( "Newspapers	95	200	121	400	816<BR>\n" );
document.write( "Television	136	127	135	211	609<BR>\n" );
document.write( "Social Media	155	99	170	146	570<BR>\n" );
document.write( "Grapevine	250	155	95	25	505<BR>\n" );
document.write( "Total	636	561	521	782	2500<BR>\n" );
document.write( "a. State both the null and alternative hypotheses. [2 marks]\r<BR>\n" );
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document.write( "b. Provide the decision rule for making this decision. Use an alpha level of 5%. [2 marks]\r<BR>\n" );
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document.write( "c. Show all of the work necessary to calculate the appropriate statistic. [5 marks]\r<BR>\n" );
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document.write( "d. What conclusion are you allowed to draw? [2 marks]\r<BR>\n" );
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document.write( "e. Would your conclusion change at the 10% level of significance? [2 marks]\r<BR>\n" );
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document.write( "f. Confirm test results in part (c) using JASP. Note: All JASP input files and output tables should be provided [3 marks] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848074 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=848074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a. State the null and alternative hypotheses.**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** There is no association between the main source of news and the educational level of individuals. <BR>\n" );
document.write( "* **Alternative Hypothesis (Ha):** There is an association between the main source of news and the educational level of individuals.\r<BR>\n" );
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document.write( "**b. Decision Rule (α = 0.05)**\r<BR>\n" );
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document.write( "* We will use a Chi-Square test for independence. <BR>\n" );
document.write( "* Find the critical value of Chi-Square (χ²) from the Chi-Square distribution table with degrees of freedom: (rows - 1) * (columns - 1) = (4 - 1) * (4 - 1) = 9. <BR>\n" );
document.write( "* The critical value for χ² with 9 degrees of freedom at α = 0.05 is 16.919.<BR>\n" );
document.write( "* **Decision Rule:** Reject the null hypothesis (H0) if the calculated Chi-Square test statistic is greater than 16.919.\r<BR>\n" );
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document.write( "**c. Calculate the Chi-Square Test Statistic**\r<BR>\n" );
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document.write( "1. **Calculate Expected Frequencies:**\r<BR>\n" );
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document.write( "   * Expected Frequency for each cell = (Row Total * Column Total) / Grand Total\r<BR>\n" );
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document.write( "   | Source of News | Primary | Secondary | Graduate | Post Graduate | Row Total |<BR>\n" );
document.write( "   |---|---|---|---|---|---|<BR>\n" );
document.write( "   | Newspapers | (816 * 636) / 2500 = 207.17 | (816 * 561) / 2500 = 182.81 | (816 * 521) / 2500 = 169.73 | (816 * 782) / 2500 = 253.30 | 816 |<BR>\n" );
document.write( "   | Television | (609 * 636) / 2500 = 154.60 | (609 * 561) / 2500 = 136.29 | (609 * 521) / 2500 = 127.03 | (609 * 782) / 2500 = 191.08 | 609 |<BR>\n" );
document.write( "   | Social Media | (570 * 636) / 2500 = 144.72 | (570 * 561) / 2500 = 127.51 | (570 * 521) / 2500 = 119.03 | (570 * 782) / 2500 = 178.74 | 570 |<BR>\n" );
document.write( "   | Grapevine | (505 * 636) / 2500 = 128.51 | (505 * 561) / 2500 = 113.39 | (505 * 521) / 2500 = 105.21 | (505 * 782) / 2500 = 157.90 | 505 |<BR>\n" );
document.write( "   | Column Total | 636 | 561 | 521 | 782 | 2500 |\r<BR>\n" );
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document.write( "2. **Calculate the Chi-Square Statistic:**\r<BR>\n" );
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document.write( "   * χ² = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]\r<BR>\n" );
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document.write( "   * Calculate this for each cell in the table and sum them up.\r<BR>\n" );
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document.write( "3. **Find the Degrees of Freedom:**\r<BR>\n" );
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document.write( "   * Degrees of Freedom (df) = (Rows - 1) * (Columns - 1) = 3 * 3 = 9\r<BR>\n" );
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document.write( "**d. Conclusion**\r<BR>\n" );
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document.write( "* Compare the calculated Chi-Square statistic to the critical value (16.919).<BR>\n" );
document.write( "    * If the calculated Chi-Square statistic is greater than 16.919, reject the null hypothesis. <BR>\n" );
document.write( "    * If the calculated Chi-Square statistic is less than or equal to 16.919, fail to reject the null hypothesis.\r<BR>\n" );
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document.write( "**e. Conclusion at the 10% level of significance:**\r<BR>\n" );
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document.write( "* Find the critical value of Chi-Square for α = 0.10 with 9 degrees of freedom (from the Chi-Square distribution table).<BR>\n" );
document.write( "* Compare the calculated Chi-Square statistic to this new critical value.<BR>\n" );
document.write( "* If the calculated Chi-Square statistic is greater than the new critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.\r<BR>\n" );
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document.write( "**f. Confirm Test Results in JASP**\r<BR>\n" );
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document.write( "1. **Input Data:** <BR>\n" );
document.write( "   * Enter the observed frequencies into JASP.<BR>\n" );
document.write( "   * Specify the row and column variables.\r<BR>\n" );
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document.write( "2. **Run Chi-Square Test:**<BR>\n" );
document.write( "   * Go to \"Frequencies\" -> \"Contingency Tables.\"<BR>\n" );
document.write( "   * Select the appropriate variables.<BR>\n" );
document.write( "   * Choose \"Chi-Square\" under \"Statistics.\"<BR>\n" );
document.write( "   * Click \"Run Analysis.\"\r<BR>\n" );
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document.write( "3. **Interpret JASP Output:**<BR>\n" );
document.write( "   * JASP will provide the calculated Chi-Square statistic, degrees of freedom, and the p-value.<BR>\n" );
document.write( "   * Compare the p-value to the significance level (0.05 and 0.10).<BR>\n" );
document.write( "   * If the p-value is less than the significance level, reject the null hypothesis.\r<BR>\n" );
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document.write( "**JASP Input and Output:**\r<BR>\n" );
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document.write( "* **Input:** <BR>\n" );
document.write( "    * You would input the observed frequencies from the table into JASP. <BR>\n" );
document.write( "* **Output:**<BR>\n" );
document.write( "    * JASP will provide a table with the following information:<BR>\n" );
document.write( "        * Chi-Square statistic<BR>\n" );
document.write( "        * Degrees of freedom<BR>\n" );
document.write( "        * p-value <BR>\n" );
document.write( "        * Expected frequencies (for comparison)\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This analysis assumes that the data meets the assumptions of the Chi-Square test (e.g., expected frequencies in each cell are sufficiently large). \r<BR>\n" );
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document.write( "I hope this comprehensive explanation is helpful!<BR>\n" );
document.write( " </SPAN>\n" );
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