Q1. Dexterity of musicians

Q1. Dexterity of musicians This question may be handwritten and then scanned to pdf, or typed up. A study was conducted to compare finger dexterity of music students who study piano to those who study singing. A random sample of 137 students from the piano group had mean dexterity score of 37.25 and standard deviation 4.34. An independent sample of 137 singing students had mean dexterity score of 35.91 and standard deviation of 5.19. Let uj and /2 denote the true mean dexterity score of piano students and singing students, respectively. (a) Test to see whether there is sufficient evidence in the sample to indicate that piano students have a higher mean dexterity score than singing students. You may use a significance level of 0.05. [4 marks] (b) Calculate the power of the test used in part (a) when /1 - /2 = 3. [4 marks] (c) Find the sample size needed for the test to achieve a significance level of 0.05 and power of 0.95, when M1 - /2 =3. You may assume equal sample size for both groups. [2 marks]