Use this TEMPLATE to submit your Unit 9 Assignment 2. (Yes, you must use this!) Be sure to see my worksheet named "Example" for examples on filling the template. (The "Example" worksheet is visible at the bottom.) I have shown every type of situation, so try to model your results after the ones shown. When determining the two hypothesis for each question, how do you know "what" to compare the population parameter to? Honestly, we don't! But, we can make an educated guess. First, since we have sample proportions and means to consider, remember that the sample statistics always supports the ALTERNATE hypothesis . (Why? Hypothesis testing always tries to reject the null hypothesis, thus we must have some evidence (the sample statistics) that the alternate is correct. Outside of this requirement, feel free to use any "logical" value in your hypothesis test. A few notes, however: 1. We always think the alternate hypothesis is correct! This means the sample statistics (sample proportion or mean) supports the alternate hypothesis. 2. You probably want to WRITE the alternate hypothesis first. Then, the null is just the opposite. (Our textbook always shows just = on the null, but it should be the opposite of the alternate.) 3. The SAMPLE proportion or mean (from the survey) never shows up in the hypotheses. 4. On Questions 1-4, we are using the Sample PROPORTION to estimate the Population PROPORTION; on Questions 5-6, we are using the Sample MEAN to estimate the Population MEAN. Thus, we use different formulas for their confidence intervals, and for their test statistics in the hypothesis tests. 5. The two hypotheses MUST be the exact opposites of each other. We can not put one value in Ho and another in Ha; that simply isn't logical. 6. Make sure your FORMULAs show up in the formula area. DO NOT replace formulas with numbers. I must be able to see "how" you calculate your confidence intervals and test statistics! Your Unit 9 Assignment 2 MUST be submitted using this Template. Feel free to add additional work at the bottom, but the top must remain. Be sure to post questions inside the "Ask Instructor" discussion topic. Note: See the Worksheet named "Example" (visible at bottom) for examples of how to fill-in the yellow boxes. Statistical Summary Sample Question Proportion #1 #2 #3 #4 Question #5 #6 Sample Mean Confidence Intervals Sample Size Sample Std Dev Question #1 #2 #3 #4 Sample Size Error Lower Limit Upper Limit Conclusion Question #5 #6 Error Lower Limit Upper Limit IMPORTANT: Make sure you SHOW the FORMULA in these columns! (Don't just put a "number" here.) I must be able to see "how" you calculate these cells. (The formula MUST appear next to the fx label! See my "Example" worsheet.) Click on the arrows and this text-box, then press DELETE to erase them. Conclusion Hypothesis Tests Question Ho #1 p #2 p #3 p #4 p #5 #6 Ha p p p p Reject Ho when Rejection criteria: Left tailed test, reject Ho when z < -1.645 Right tailed test, reject Ho when z > 1.645 Two tailed test, reject Ho when z < -1.96 or z > 1.96 Test Statistic Decision Summary IMPORTANT: Be sure you CHANGE the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha!! In the current-formula, the population proportions are shown as 0.55, 0.50, 0.60 for the first three questions. My work below uses made-up data. Remember that the value you use in your hypotheses is UP TO YOU!! You can compare your population parameters to any value, just remember that the sample statistic must AGREE with your alternate hypothesis. We always try to reject the null hypothesis, so that means we must have evidence (via the sample statistic) that the alternate hypothesis is true. Click on a CELL to see the FORMULA used Statistical Summary Sample Sample Question Proportion Size #1 0.61 31 #2 0.45 31 #3 0.45 31 #4 0.42 31 Question #5 #6 Sample Sample Sample Mean Std Dev Size 0.52 8.39 31 0.84 2.77 31 Remember that the values used in the hypotheses are "whatever" you want; just make sure the sample statistic supports Ha! FORMAT HINT: Copy the "math" notation to another cell using copy, then paste. Right-click the cell to see these options. IMPORTANT: Make sure you DO NOT replace the formula with a "number". I must be able to see "how" you calculate these cells. (The formula MUST appear next to the fx label! Confidence Intervals Lower Error Limit 0.1752049491 0.434795051 0.178705019 0.2712949808 0.178705019 0.2712949808 0.1772914495 0.242708551 Upper Limit 0.7852049491 0.6287050192 0.6287050192 0.5972914495 Conclusion We are 95% confident We are 95% confident We are 95% confident We are 95% confident Lower Question Error Limit #5 3.013776968 -2.493776968 #6 0.9950133732 -0.155013373 Upper Limit 3.533776968 1.8350133732 Conclusion We are 95% confident the true population mean is between 14.72 and 15.92. We are 95% confident the true population mean is between 118.17 and 123.95. Question #1 #2 #3 #4 Hypothesis Tests Question Ho #1 p 0.55 #2 p 0.50 #3 p = 0.60 #4 p 0.75 #5 = 17 #6 119 Ha p < 0.55 p > 0.50 p 0.60 p < 0.75 17 > 119 Reject Ho when z < -1.645 z > 1.645 z < -1.96 or z > 1.96 z < -1.645 z < -1.96 or z > 1.96 z > 1.645 Rejection criteria: Left tailed test, reject Ho when z < -1.645 Right tailed test, reject Ho when z > 1.645 Two tailed test, reject Ho when z < -1.96 or z > 1.96 the true population proportion is between 0.293 and 0.547 the true population proportion is between 0.604 and 0.836. the true population proportion is between 0.453 and 0.707. the true population proportion is between 0.527 and 0.773. Test Statistic Decision 0.6714976477 Reject Ho -0.5567764363 Reject Ho -1.7047727121 Do not Reject Ho -4.2432063348 Reject Ho -10.9364429916 Reject Ho -237.5043455278 Do not Reject Ho Summary There is sufficient statistical evidence to show the population proportion is less than 0.55. There is sufficient statistical evidence to show the population proportion is greater than 0.50. There is not sufficient statistical evidence to show the populaton proportion is not 0.60. There is sufficient statistical evidence to show the population proportion is less than 0.75. There is sufficient statistical evidence to show the population mean is not 17. There is not sufficient statistical evidence to show the population mean is greater than 119. IMPORTANT: Be sure you CHANGE the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha!! In the current-formula, the population proportions are shown as 0.55, 0.50, 0.60 for the first three questions