2. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.A. There must be an expected count of at least 5 in every cell of the table.|B. The sample size must be at least 30 or the population data must be normally distributed.|C. There must be at least 10 "success" and 10 "failure" observations.D. The observations must be independent of one another.3. What is the expected value for the number of Black drivers who were not wearing a seat belt?Expected value =4. State the degrees of freedom for this test.df =5. Calculate the test statistic:6. What was the contribution toward this test statistic of Black drivers who were not wearing a seat belt?Test statistic =7. Calculate the p-value for this test.p = Buckle up! - How does seat belt use vary with drivers' ethnic group? It is well known that location and gender (males are less likely to buckle up) arefactors. Here is the data and the mosaic plot for a random sample of male drivers observed in Houston.Ethnic group of driver BeltedNot Belted TotalBlack27799376Hispanic373164537White19762259Total8473251172EthnicityHispanicBlackWhiteUse of Seat Beltwearing a seat beltnot wearing a seat belt

Solution: The observed count table is Ethnic group of driver Belted Not Bleted Row Total Black 277 99 376 Hispanic 373 164 537 White 197 62 259 Column Total 847 325 11722) Condition for the hypothesis test are There must be an expected count of at least 5 in every cell of the table. The observation must be independent of one another. Option A and D are correct. 3) The expected number of Black drivers who were not wearing seat belt is Expected value = Row Total of black driver×Column total of not beltedTotal Expected value = 376×3251172Expected value = 104.27 The expected number of Black drivers who were not wearing seat belt is 104.27 4) To find degree of freedom for this test. r= 3 number of row c= 2 number of column Degree of freedom =df= (r-1)*(c-1) df= ( 3-1)*(2-1) df= 2*1= 2 5) To find the expected value table. The expected value can be determine as give by Expected value = Row Total ×Column TotalTotal The expected table is Ethnic group of driver Belted Not Bleted Row Total Black 376×8471172=271.73 104.27 376 Hispanic 388.09 148.91 537 White 187.18 71.82 259 Column Total 847 325 1172 Test statistic χ2=∑(O-E)2E O E (O-E)2 (O-E)2E 277 271.73 27.7729 0.102208 373 388.09 227.7081 0.58674 197 187.18 96.4324 0.515185 99 104.27 27.7729 0.266356 164 148.91 227.7081 1.529166 62 71.82 96.4324 1.342696 Where O = observed value and E = Expected value ∑(O-E)2E=4.342351χ2=4.3424 The value of test statitic is 4.3424 6) To find the contribution of of Black drivers who were not wearing seat belt. Contribution test statistic = ( Observed value of black driver not belted- expected value of black driver not bleted)2 Expected value of black driver not bletedContribution test statistic =(99-104.27)2104.27Contribution test statistic = 0.266356 The contribution of of Black drivers who were not wearing seat belt is 0.266356 7) To find p value p value = P(χ2> 4.3424) p value = 0.1140 From Excel The p value for the test is 0.1140