Q4. Sample surveys conducted in a large country in a certain year and again 20 years later showed that originally the average height of 420 ten-year-old boys was 54 inches with a sam- ple standard...

Plzz solve i) and ii) and explain

Extracted text: Q4. Sample surveys conducted in a large country in a certain year and again 20 years later showed that originally the average height of 420 ten-year-old boys was 54 inches with a sam- ple standard deviation of 2.8 inches. On the other hand, 20 years later, the average height of 480 ten-year-old boys was 56 inches with a sample standard deviation of 2.4 inches. Test the hypothesis Ho : 41 – 42 = -0.5 against the alternative H1 : 41 - 42 < -0.5="" at="" 0.05="" level="" of="" significance="" where="" 41="" and="" 2="" are="" the="" true="" average="" heights="" of="" boys="" 20="" years="" before="" and="" after,="" respectively.="" suppose="" the="" populations="" are="" normally="" distributed.="" (i).="" test="" the="" hypothesis="" by="" finding="" the="" critical="" region.="" (ii).="" test="" the="" hypothesis="" by="" finding="" the="" p-value="" (note="" that="" you="" do="" not="" need="" to="" find="" the="" exact="" p-value="" from="" the="" table.="" but,="" you="" can="" still="" conduct="" the="">