Decide and state whether a one-sample z test, a two- sample ztest, or a t test is appropriate. Whichever test you choose, stateyour null hypothesis, then obtain a P -value and formulate a validconclusion.

1a.) 20 subjects who do not speak German are asked toparticipate in a trial for a new type of crash course in the Germanlanguage. 10 subjects are randomly placed in Group A, to test thenew teaching method, while the other 10 are placed in group B andgiven a more traditional crash course in German (though they arenot told this is not the new approach). After both courses haveended, evaluators (who don’t know which course each subject took)determine that 50% of subjects in Group A are competent speakers ofGerman, compared to 40% of subjects in Group B. Based on this, doesthe new method work better, or is the 10% difference due tochance?

1b.) 200 subjects who do not speak German participate in a trialfor a new type of crash course in the German language. 100 subjectsare randomly placed in Group A, to experience the new teachingmethod, while the other 100 are placed in group B and given a moretraditional crash course in German (though they are not told thisis not the new approach). After both courses have ended, evaluators(who don’t know which course each subject took) determine that 42%of subjects in Group A are competent speakers of German, comparedto 38% of subjects in Group B. Based on this, does the new methodwork better, or is the 4% difference merely due to chance?