Question

A guidance counselor claims that the high school students in a college preparation program have higher ACT scores than those in a general program. The sample mean ACT scores for 37 high school students in a college prep program is 22.7 and assume the population standard deviation is 3.5. The sample mean ACT scores for 35 high school students in a general prep program is 21.1. Assume the population standard deviation is 4.9. At  = 0.02 , test the counselor’s claim. • Suppose 1 represents the mean ACT score of all college prep students • Suppose  2 represents the mean ACT score of all general prep students

1). State the hypothesis and label which represents the claim: : H 0 : H a

2). Specify the level of significance  =

3). Sketch the appropriate distribution, find and label the Critical Value(s) in Statdisk to 3 decimal places, and shade in  to indicate the Rejection Region(s).

4). Calculate the test statistic. Label this appropriately as Z or t.

5). Decision:

6). Write a statement to interpret the decision in the context of the original claim

Answer 1

Ang X= 22.7, z = 261, 0,- 3.5, 02= 409, nie 37, n2=35 d20.02 © Hypothesisi Hoi 41 = 42 Hi el>ll2 (claim). E (2) Level of significance (x) = 0.02 - ol. Critical Valcea K=0,02 = 0 2 = 2,0 54 (from Zutable) 2.054 i Rejection Rogion )Appropriate teststatistics is Z-test because popielatim standard deviations are known ond ni 2n 22,80. Test statistics - 2 NIO, z = - 2 62 - 22:7 - 261 z=22 1.5865 3.52 4.92 37 35 Z= 1.587 (5) Decision: Since, Z=1.587 < Zac 2.054 Hence, we fail to reject Ho at p=0.02 61. There is no evidence to support the claim that the ACT scores are higher in preporation program than general program,