If you could answer and explian that be great a It is claime

If you could answer and explian that be great

a) It is claimed that the mean time for college students to complete this task (without exercise) is 30 seconds with standard deviation of 3 seconds. Given that the sample mean is 29.1 seconds for a sample of size 50, is there convincing evidence that 15 minutes of vigorous exercise reduces (less than, 1-sided test) the time needed to complete the task? Perform a test of significance, stating the p-value and your conclusion regarding the value of exercise on hand/eye coordination. Use an alpha level of .05.

b) Suppose the alpha level was now set at .01, then state your revised conclusion regarding the p-value you obtained in the previous problem.

c) Suppose the experiment was designed to test whether the time to complete the task with vigorous exercise was different than (not equal to, 2 sided test) the time to complete the task without exercise. How would the p-value of the experiment change? (Hint: In problem 30, we believe that vigorous exercise will reduce the time to complete the task).

Solution

a)Set Up Hypothesis
Null Hypothesis H0: U>30
Alternate Hypothesis H1: U<30
Test Statistic
Population Mean(U)=30
Given That X(Mean)=29.1
Standard Deviation(S.D)=3
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=29.1-30/(3/Sqrt(50)
Zo =-2.1213
| Zo | =2.1213
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.1213 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -2.1213 ) = 0.0169
Hence Value of P0.05 > 0.0169, Here we Reject Ho

Yes, it reduced the task

b)
P-Value : Left Tail - Ha : ( P < -2.1213 ) = 0.0169
Hence Value of P0.01 < 0.0169, Here We Do not Reject Ho\"
No, its nt reduced
c)
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -2.1213 ) = 0.0339
Hence Value of P0.01 < 0.0339, Here We Do not Reject Ho

No, its nt reduced