A researcher surveyed randomly selected Democrats and Republicans asking them what the number one concern should be for the president of the United States. The results of the survey are shown below. Is there evidence to conclude that there is a difference in what Democrats and Republicans think is the most important? EconomyForeign AffairsFamily ValuesEnvironmentOtherDemocrats82588070 44 Republicans106789457 38 What can be concluded at the αα = 0.05 significance level?What is the correct statistical test to use?Goodness-of-FitIndependenceHomogeneityPaired t-testThe test-statistic for this data = (Please show your answer to three decimal places.)The p-value for this sample = (Please show your answer to four decimal places.) The p-value is αα

χ2=∑fo-fe2fe~ (rows-1)×(columns-1) df where, fo is the observed count fe is the expected count state hypotheses : Null hypothesis Ho : There is no difference in what Democrats and Republicans think is the most important Alternative Hypothesis Ha : There is a difference in what Democrats and Republicans think is the most important a) What is the correct statistical test to use Chi square χ2 Goodness-of-Fit is correct statistical test to use. Because, this test helps to compare the proportion in each category differ from the expected proportion (or) not. So, Goodness-of-Fit is correct statistical test to use b) The test-statistic for this data is Given data table is Observed frequency (fo) Economy(1) Foreign Affairs (2) Family Values(3) Environment(4) Other(5) Row total Democrats (1) 82 58 80 70 44 334 Republicans(2) 106 78 94 57 38 373 Column total 188 136 174 127 82 N = 707 Find the expected frequencies for each cell fe=Column total ×Row totalNthen, f1,1=188×334707 =88.815, f1,2=136×334707 =64.249, f1,3=174×334707 =82.201, f1,4=127×334707 =59.997, f1,5=82×334707 =38.738 f2,1=188×373707 =99.185, f2,2=136×373707 =71.751, f2,3=174×373707 =91.799, f2,4=127×373707 =67.003, f2,5=82×373707 =43.262 expected frequencies ( fe) Economy Foreign Affairs Family Values Environment Other Row total Democrats 88.815 64.249 82.201 59.997 38.738 334.000 Republicans 99.185 71.751 91.799 67.003 43.262 373.000 Column total 188.000 136.000 174.000 127.000 82.000 N = 707.000 test statistic calculated as χ2=82-88.815288.815+58-64.249264.249+80-82.201282.201+70-59.997259.997+44-38.738238.738 +106-99.185299.185+78-71.751271.751+94-91.799291.799+57-67.003267.00338-43.262243.262 =6.770 Therefore, the test-statistic for this data is 6.770 c) The p-value for this sample is Calculation of p value: if chi square test χ2 = 6.770 with df = 4 then p value is 0.1485 [ Refer chi square distribution p table values] [Here df = No of (Rows – 1)*(columns -1) = (2-1)*(5-1) = 4 ] The p-value for this sample is 0.1485 d) The p value (0.1485) is greater than or equal to αα = 0.05 So, don’t reject Ho. There is not sufficient evidence to conclude that there is a difference in what Democrats and Republicans think is the most important.