*Note: For problems 1 - 4, complete the 5step process: Step 1: State the null hypothesis and the alternate hypothesis. Step 2: Select the level of significance. Step 3: Evaluate the test statistic. Step 4: Formulate a decision rule with critical value of test statistic. Step 5: Compare the test statistic to the critical value and make the decision about H0. 1. Hypothesis testing with 2 populations: UMUC's Business Management department is concerned that dual degree students may be receiving lower grades than the regular management students. Two independent random samples have been selected. 150 observations from population 1 (dual degree students) and 150 from population 2 (management only degree.) It is known from past studies that the population variance for dual degree students is 4.5 and the population variance for management only students is 5.0. The current study found that the mean score for the dual degree students is 79 and the mean score for the management only students is 82. Is there evidence that the dual degree students are receiving lower grades than regular management students? 2. F-Test Two-sample for Variances Use Excel's 2-sample variances data analysis tool to solve the following problem. A well-known ice cream store wants to test two different methods for scooping ice cream so they can use the one that has the least variability in their training of new and current employees. It took a sample of the ice cream cones scooped and measured the weights. Use the F-Test Two-Sample for Variances to test the hypothesis that the variances between the two methods are the same. Interpret the results. Method 1 4.7 3.7 3.2 3.1 3.9 4.8 3.1 5.1 4.9 5.3 2.8 4.2 Method 2 3.7 4.1 3.5 5.5 4.1 4.7 4.9 3.5 3.9 3.7 4.8 5 5.3 4.4 4.6 3. Hypothesis testing using the p value: The hypothesis is that the mean IQ of the population is 100. A random sample of six IQs in this population resulted in the following values: 118, 105, 112, 119, 105, and 111. Using the .05 significance level, is it possible to conclude that the mean is different from 100? a. State the decision rule. b. Compute the test statistic c. What is your conclusion? d. Use Excel to find the p-value. What does it mean? 4. Hypothesis testing on a proportion: The administration of UMUC is concerned that a significant number of their students are not graduating in 4 years. One factor that may contribute to the low graduation rate after 4 years could be the number of students that change their majors after the first year at UMUC. A nationwide study found that about 50% of first year students at any university change their major after the first year. UMUC sampled 100 students and found that 48 had changed their major after their first year. At the .05 level, is the proportion of students at UMUC that change their major higher than 50%? 5. Scatter Plots: Graph each set of data using the xy chart feature in Excel. Add the chart name, Axes descriptions, r squared, and the linear equation to your chart. a. Highest Grossing movies and the year they were released. $2,186.80 1997 $2,068.20 2015 $1,670.40 2015 $1,519.60 2012 $1,516.00 2015 $1,405.40 2015 $1,341.50 2011 $1,276.50 2013 $1,215.40 2013 $1,159.40 2015 $1,151.10 2016 $1,123.80 2011 $1,119.90 2003 $1,108.60 2012 $1,104.10 2014 $1,084.90 2012 $1,066.20 2006 $1,063.20 2010 $1,045.70 2011 $1,029.20 1993 $1,027.00 1999 $1,025.50 2010 $1,022.60 2016 $1,021.10 2012 $1,004.60 2008 $974.80 2001 $970.80 2013 $968.50 1994 $963.40 2007 $960.30 2010 $958.40 2013 $956.00 2014 $939.90 2007 $937.90 2016 $936.70 2003 $934.40 2009 $926.00 2002 $919.80 2004 $896.90 2005 $890.90 2007 $886.70 2009 $880.70 2015 $879.00 2002 $877.20 2012 $872.70 2016 $871.50 2001 $865.00 2013 $857.40 2015 $848.80 2005 $836.30 2009 $829.70 2012 $825.50 2010 $821.70 2002 $817.40 1996 $799.00 2007 $796.70 2004 $792.90 1982 $788.70 2013 $786.60 2008 $783.80 2004 $782.40 2016 $775.40 1977 $773.30 2014 $769.70 2009 $758.50 2014 $758.20 2006 $757.90 2012 $755.40 2014 $752.60 2010 $747.90 2014 $746.90 2012 $745.00 2005 $743.60 2013 $742.10 2003 $731.30 2009 $727.60 2016 $723.20 2013 $714.40 2014 $712.20 2011 $710.60 2014 $709.70 2009 $709.70 2007 $709.00 2014 $698.50 2010 $694.70 2011 $694.40 2012 $682.30 2015 $677.90 1994 $675.10 2014 $672.80 1999 $668.00 2013 $665.70 2011 $660.90 2006 $657.80 2014 $654.30 2003 $653.40 2015 $649.40 2002 $644.60 2013 $631.70 2008 b. Hours studied and test grade 3 5 2 6 7 75 90 75 80 90 1 2 7 1 7 2 6 7 1 5 5 5 3 3 9 5 6 2 5 2 3 8 4 5 6 50 65 85 40 100 70 85 85 70 80 85 80 50 60 95 75 80 50 65 40 70 80 75 60 95 c. Humidity level and time spent outside 50% 40% 70% 20% 90% 30% 70% 30% 20% 30% 40% 10% 90% 6 7 0.5 4.5 0.25 4 5.5 2 2 2.75 2.75 8.5 1 70% 80% 50% 70% 40% 30% 20% 20% 70% 70% 80% 50% 2.2 1.5 3 1.25 4 3.75 6 5 2.5 2 1 4