Quest 14 pts D Question 3 A math teacher claims that taking

Quest 14 pts D Question 3 A math teacher claims that taking both geometry and algebra kads to less Varation in ACT scores. The mesn ACT score is 21.2, and standard dewation of the population is 4.9 The math Teachar takes a sandom sample of 25 students who have taken both couses gives a mean ACT score of 21.9 and standard deviation of 3.8. The clairmed (al Test ths claim at the a-05 lavel (by In addition to your conclusion, dentily a kurtkng varisble that could have infuenced this study, c) What assumptions needed to be met in ader for the teacher to sun theis hypothesis test? Time Run t Hour, 40 ·e eì H-TT. Font sues Paragraph .

Solution

Set Up Hypothesis
Null, no clue to prove the assumption H0: U=21.2
Alternate, taking both geometry, algebra lead to less variation in ACT score H1: U>21.2
Test Statistic
Population Mean(U)=21.2
Given That X(Mean)=21.9
Standard Deviation(S.D)=4.9
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=21.9-21.2/(4.9/Sqrt(25)
Zo =0.7143
| Zo | =0.7143
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.7143 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 0.7143 ) = 0.2375
Hence Value of P0.05 < 0.2375, Here We Do not Reject Ho

we don\'t have evidenc eto cliam taking both geometry, algebra lead to less variation in ACT score