Chapter 10: Hypothesis Testing Using a Single Sample Concept Quiz
Name ______
The following questions are in a True / False format. The answers to these questions will frequently depend on remembering facts, understanding of the concepts, and knowing the statistical vocabulary. Before answering these questions, be sure to read them carefully!
T F 1. The statement is a statistical hypothesis.
T F 2. The choice of the alternative hypothesis depends on the objectives of the study.
T F 3. If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.
T F 4. A type II error is made by failing to reject a false null hypothesis.
T F 5. The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.
T F 6. All other things being equal, choosing a smaller value of will increase the probability of making a type II error.
T F 7. Small P-values indicate that the observed sample is inconsistent with the null hypothesis.
T F 8. It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than .
T F 9. The power of a test is the probability of failing to reject the null hypothesis.
T F 10. is called the observed significance level.
T F 11. For tests of hypotheses about , decreases as the sample size increases if the level of significance stays the same.
Chapter 10, Review Packet Page 1 of 7 Chapter 10: Hypothesis Testing Using a Single Sample Section 10.1-10.2
Name ______
1. Explain in your own words what a hypothesis test is.
2. Explain in your own words the distinction between a null and alternative hypothesis.
Chapter 10, Review Packet Page 2 of 7 3. Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after an interval of time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory situation, where the child is away from the familiar setting of home. Let denote the proportion of 2-year-olds than have this understanding in the home situation, and suppose that . The investigators wish to determine whether the proportion that remembers is less when the child is away from home. a) What is the appropriate null hypothesis?
b) What is the appropriate alternative hypothesis?
c) In your own words, distinguish between a Type I and a Type II error in this context.
Chapter 10, Review Packet Page 3 of 7 4. The Environmental Protection Agency (EPA) is charged with monitoring the environment. One aspect of this is keeping track of "acid rain," a broad term describing the fall of water through an acidic atmosphere. Acidity is measured on the pH scale, where pure water has a pH of 7.0. Normal rain is slightly acidic because carbon dioxide dissolves into it, and thus has a pH of about 5.5. (A lower pH indicates greater acidity.) Suppose the EPA wishes to determine whether a particular area is subject to acid rain. Let denote the true average for pH in this area. a) What is the appropriate null hypothesis?
b) What is the appropriate alternative hypothesis?
c) In your own words, distinguish between a Type I and a Type II error in this context.
Chapter 10, Review Packet Page 4 of 7 Chapter 10: Hypothesis Testing Using a Single Sample Section 10.3-10.4
Name ______
1. Define, using your own words, a test statistic.
2. In your own words, what is a P-Value?
Chapter 10, Review Packet Page 5 of 7 3. As children grow they develop what is known as "representational insight," a connection between an object and a symbol for that object. A random sample of youngsters 24-months old were shown a video of someone putting a toy under 1 of 4 randomly placed boxes in a room familiar to the child. They were then taken to the room, and asked to "find the toy." The investigators reasoned that a child with representational insight should pick the correct box on the first try. If the children were to overturn the boxes randomly, they would find the toy on the first turn 25% of the time. Thirty children out of 57 subjects found the toy by turning over the correct box on the first try.
Does this sample provide sufficient evidence that the proportion of 24-month old children who choose the correct box on the first try is greater than 0.25? Use a significance level of to test the appropriate hypothesis.
Chapter 10, Review Packet Page 6 of 7 4. The department of natural resources defines a fish to be unsafe to eat if the polychlorinated biphenol (PCB) concentration exceeds 5 parts per billion (ppb). A random sample of 10 fish taken from a local lake resulted in the data listed below:
2.6, 6.6, 4.8, 5.4, 5.1, 4.5, 6.9, 4.9, 3.7, 3.8
Is there sufficient evidence to conclude that the mean PCB concentration for fish from this lake exceeds 5 ppb?
Chapter 10, Review Packet Page 7 of 7