Ms FitnessBuff a high school gym teacher wants to propose an

Ms. Fitness-Buff, a high school gym teacher, wants to propose an after school fitness program. To get an idea of the fitness level of the student at her school, she takes a random sample of 75 students and records the number of hours the students exercised in the past week. Her sample mean in 2.25 hours and she knows from past research that the population standard deviation is 2 hours. She wants to know if this varies from a population mean of 3 hours per week.

What would the consequences of a Type II error be for the test from part C?

What is the rejection region for Ho: mue = 3 for the test from part C?

Calculate the probability of making a Type II error if the true population mean is 2.75.

What\'s the power of the test if the true population mean is 2.75?

Solution

Set Up Hypothesis
Null Hypothesis H0: U = 3
Alternate Hypothesis H1: U!=3
Test Statistic
Population Mean(U)=3
Sample X(Mean)=2
Standard Deviation(S.D)=10
Number (n)=75
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =2-3/(10/Sqrt(74))
to =-0.866
| to | =0.866
Critical Value
The Value of |t a| with n-1 = 74 d.f is 2.288
We got |to| =0.866 & | t a | =2.288
Make Decision
Hence Value of |to | < | t a | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -0.866 ) = 0.3893
Hence Value of P0.025 < 0.3893,Here We Do not Reject Ho

power of the test = 1- Type 2 Error = 1 - 0.3893 = 0.6107