1. Suppose we are testing H0: μ = 10 versus Ha: μ < 10. This chart shows the results.
The upper right hand curve represents the sampling distribution of x¯ when H0 is true; the lower left hand curve represents the sampling distribution of x¯ when Ha is true.
What is the color of the area that represents if μ is really 10?
beige (area to the right of the line on the top curve)
green (area to the left of the line on the bottom curve)
red (area to the left of the line on the top curve)
light blue (area to the right of the line on the bottom curve)
2. If we set = 0.05, what can we do to increase power?
increase sample size
decrease sample size
increase the probability of a type II error
Use this information to answer the next three questions.Your company markets a computerized medical diagnostic program used to evaluate thousands of people. The program scans the results of routine medical tests (pulse rate, blood tests, etc.) and refers the case to a doctor if there is evidence of a medical problem. The program makes a decision about each person. The hypotheses are:
- H0: The patient is healthy.
- Ha: The patient has a medical problem.
3. Which of the following describes a type I error in this situation?
-not referring a patient with a medical problem to the doctor
-sending a healthy patient to the doctor
-sending a patient with a medical problem to the doctor
-not referring a healthy patient to the doctor
4. Which of the following describes a type II error in this situation?
sending a patient with a medical problem to the doctor
not referring a healthy patient to the doctor
not referring a patient with a medical problem to the doctor
sending a healthy patient to the doctor
5. Suppose you work for an insurance company which covers these types of routine doctor visits for some of its policy holders. The company desires to minimize costs by not sending a healthy patient to a doctor. Which error probability would you choose to make smaller?
type II error probability
type I error probability
6. Which of the following describes statistical power in this situation?
the probability of sending a healthy patient to the doctor
the probability of sending a patient with a medical problem to the doctor
the probability of not referring a healthy patient to the doctor
the probability of not referring a patient with a medical problem to the doctor
Use this information to answer the next four questions.A certain prescription medicine is supposed to contain an average of 250 parts per million (ppm) of a certain chemical. If the concentration is higher than this, the drug may cause harmful side effects; if it is lower, the drug may be ineffective. The manufacturer runs a check to see if the mean concentration in a large shipment conforms to the target level of 250 ppm or not. A simple random sample of 100 portions is tested, and the sample mean concentration is found to be 247 ppm. It is assumed that the concentration standard deviation in the entire shipment is σ = 12 ppm.
7. What are the appropriate null and alternative hypotheses?
H0: x¯ = 250 vs. Ha: x¯ > 250
H0: μ = 250 vs. Ha: μ ≠ 250
H0: μ = 250 vs. Ha: μ < 250
H0: x¯ = 250 vs. Ha: x¯ < 250
H0: μ = 250 vs. Ha: μ > 250
H0: x¯ = 250 vs. Ha: x¯ ≠ 250
8. Calculate the test statistic for this test.
25
-25
-2.5
2.5
9. Suppose that the test statistic was -3.00. What is the p-value for this test?
-0.0026
-0.0020
-0.0013
-0.0010
10. Suppose that the p-value was 0.0259. What is the appropriate conclusion to make if = 0.05?
-Reject H0. We have insufficient evidence to conclude that the mean concentration is less than 250 ppm.
-Reject H0. We have sufficient evidence to conclude that the mean concentration is different from 250 ppm.
-Fail to reject H0. We have insufficient evidence to conclude that the mean concentration is different from 250 ppm.
-Fail to reject H0. We have sufficient evidence to conclude that the mean concentration is less than 250 ppm.