State the hypotheses State the tail State the Critical Value

State the hypotheses

State the tail

State the Critical Value

State the p-value

Make a decision

Draw a conclusion

Men spend an average of 29 minutes per day on weekends and holidays exercising and playing sports. They spend an average of 23 minutes per day reading. A random sample of 25 men resulted in a mean of 35 minutes exercising with a standard deviation of 6.9 minutes and an average of 20.5 minutes reading with s = 7.2 minutes. Is there sufficient evidence that there two results differ from the national means?

Exercising and playing sports

N   Mean StDev SE Mean      95% CI         T      P

25 35.00   6.90     1.38 (32.15, 37.85) 4.35 0.000

Reading

N   Mean StDev SE Mean      95% CI          T      P

25 20.50   7.20     1.44 (17.53, 23.47) -1.74 0.095

Solution

I.
Set Up Hypothesis
Null, results same from the national means H0: U=29
Alternate,results differ from the national means H1: U!=29
Test Statistic
Population Mean(U)=29
Exercising Sample X(Mean)=35
Exercising Standard Deviation(S.D)=6.9
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =35-29/(6.9/Sqrt(24))
to = 4.348
| to | =4.348
Critical Value
The Value of |t | with n-1 = 24 d.f is 2.064
We got |to| =4.348 & | t | =2.064
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 4.3478 ) = 0.0002
Hence Value of P0.05 > 0.0002,Here we Reject Ho

We have evidence that Exercising results differ from the national means

II.
Set Up Hypothesis
Null, results same from the national means H0: U=29
Alternate,results differ from the national means H1: U!=29
Test Statistic
day reading Population Mean(U)=23
day reading Sample X(Mean)=20.5
Standard Deviation(S.D)=7.2
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =20.5-23/(7.2/Sqrt(24))
to =-1.736
| to | =1.736
Critical Value
The Value of |t | with n-1 = 24 d.f is 2.064
We got |to| =1.736 & | t | =2.064
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.7361 ) = 0.0954
Hence Value of P0.05 < 0.0954,Here We Do not Reject Ho

The average day reading results are same with the national means