6.) A music teacher knows from past records that 60% of students taking summer lessons play the piano. The instructor believes that this proportion may have dropped because of the popularity of wind and brass instruments. A random sample of 80 students yielded 43 piano players. Test the instructor's claim that the proportion of students taking summer lessons has dropped at a: = 0.05. a.) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? b.) Identify the sampling distribution you will use: the standard normal or the Student's tdistribution. What is the value of the sample test statistic? c.) Find (or estimate) the P value or P value range. Sketch the sampling distribution and show the area corresponding to the P value. (Alternate method: Find the critical value(s) and sketch the critical regions and the sample test statistic on the normal curve.)