Please help with part d) of this question. Show work please. Data is provided

Part d) Suppose we perform our pairwise comparisons, to test for a significant difference in the mean scores between each pair of racial groups. If investigating for a significant difference in the mean scores between blacks and whites, what would be the smallest absolute distance between the sample means that would suggest a significant difference? Assume the test is at the 5% significance level, and give your answer to 3 decimal places. 4.764361982(1 point) The Ricci v. DeStefano case in New Haven, CT (129 S. Ct. 2659, Sup. Court, 2009), involved a claim of "reverse" discrimination. Firefighters in the city took examinations to progress through the ranks. One test was for promotion to lieutenant, and at the time the city had eight such positions to fill. The city's charter required the fire department to appoint from the candidates with the best ten scores on the relevant examination. All the top ten scores were from white applicants. The district declined to certify the exam and did not promote any of the candidates, on the grounds that doing so would fail to promote sufficient visible minority candidates to an existing position. It is of interest to investigate whether there appears to be a difference in the mean scores on the examination for the three identified racial groups: white, black, and Hispanic. Suppose the test score data were as displayed below: Blacks Hispanics Whites Sample size: 19 15 43 Mean: 62.77 64.02 72.62 S.D.: 7.52 3.98 10.16