Question

1.) The scores for the final exam in Math 2250 is normally distributed with a mean of 60 and standard deviation of 15. Given that 120 students wrote the final exam, i.) State and test the hypothesis that the mean score is greater than 65 at a 10% level of significance. Include a p-value in your answer. 141 ii.) Construct and interpret 90% confidence level for the mean score. [3] Using the same level of significance, determine how many students must write the final exam to have a bound of error as 2.5. [2] ini.)

Answer 1

Giveo n120, 60, s =15 The null hypelhusis is Ho -65 The alternadive hypehusis is Ha 765 The test stat shic is 60 65 3.65 Pae P-value P(z73.GE) caitical value At x-010 1-28 CR o 1-25 Since e 2a lies in Critia Aeae z ].28 H. is geted Conclusion: There is Sutticuot evidaore to coadude that the grealte thao65 Score is Mean

The The 90 Cofideore intevaJ to populatias mean Sare is ohare 65 the t s the Syaifiaot value olat 0.10 t = 60t 1.65x 120 15 60t 2.2594 51.7406, 62 259 4 51- 74 62.26) 90 Confeleot thal the hore is Meao scre s dies 62.26 populatio betwees 5.74

Given Cenfidence leve 90/ 165 of errer E Oarsin =2 S S IS Ther 2 -G5X15 2.5 98.01 98 ta the nonber of studeots must onte thoexaro