In: Statistics and Probability
Use this scenario to answer the following questions.
Ms. Fitness-Buff, a high school gym
teacher, wants...
- Use this scenario to answer the following questions.
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 students 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 is
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/week.
- Construct a 95% confidence interval. (2
points)
- Draw a conclusion for a two-sided test at a
= .05. (1 point)
- Ms. Fitness-Buff is told that if students exercise less
than 3 hours per week, she can start an after-school fitness
program. Test this one-sided hypothesis and draw a conclusion
at a = .05. (2 points)
- What would the consequences of a Type I error be in the
test from part C? (1 point)
- What's the probability of a Type I error for the test
in part C? (1 point)
- What would the consequences of a Type II error be for
the test from part C? (1 point)
- What is the rejection region for
Ho: m = 3 for the test from part C? (1
point)
- Calculate the probability of making a Type II error if
the true population mean is 2.75. (2 points)
- What's the power of the test if the true population
mean is 2.75? (1 point)