STAT Chapter 11 Questions
*True or False* In order to determine the p-value, it is necessary to know the level of significance.
False
The critical value of the sample mean is
The smallest value of the sample mean that would cause the null hypothesis to be rejected
In a criminal trial, a Type I error is made when In a criminal trial, a Type II error is made when
an innocent person is convicted. an innocent person is acquitted.
When a null hypothesis is rejected, the test is said to be
statistically significant at level α.
The P-value is a measure of
the amount of statistical evidence that supports the alternative hypothesis.
The hypothesis testing procedure begins with the assumption that
the null hypothesis is true
In the p-value method, You reject H0 if
the p-value of your hypothesis is less than the significance level
The p-value of a test is (***)
the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.
A null hypothesis is a statement about
the value of a population parameter.
What are the two appropriate conclusions from a hypothesis test? (Summarized)
(1) Reject H0. Sufficient evidence to support H1. (2) Fail to reject H0. Insufficient evidence to support H1.
Which of the following is an appropriate null hypothesis? a) The mean of a population is equal to 60. b) The mean of a sample is equal to 60. c) The mean of a population is not equal to 60. d) All of these choices are true.
(A) The mean of a population is equal to 60. (hypotheses are testing population mean (Mu) OR population parameter (p))
A Type I error is committed if we make: (A) A Type II error is committed if we make: (B)
(A) an incorrect decision when the null hypothesis is true. (B) an incorrect decision when the null hypothesis is false.
*True or False* (***) If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level. (A) If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10 level. (B)
False (B) True
In order to determine the p-value what two things are needed? what isnt needed?
Value of test statistic and whether test is one-tail or two-tail is needed Level of significance is NOT needed
If a hypothesis is not rejected at the 0.10 level of significance, it: a) must be rejected at the 0.05 level. b) may be rejected at the 0.05 level. c) will not be rejected at the 0.05 level. d) must be rejected at the 0.025 level.
C) will not be rejected at the 0.05 level.
Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05? (***) a) 0.150 b) 0.100 c) 0.051 d) 0.025
D) 0.025 (0.05 / 2 = 0.025)
*True or False* It is possible to commit a Type I error and a Type II error at the same time.
False
*True or False* The larger the p-value, the more likely one is to reject the null hypothesis.
False
There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated. What are they?
Rejection Region method and the P-value approach
For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is:
Smaller than -1.96 or greater than 1.96 - What is the rejection region for a two tailed test?
*True or False* A Type I error is represented by α; it is the probability of rejecting a true null hypothesis.
True
*True or False* A p-value is a probability, and must be between 0 and 1.
True
*True or False* For a given level of significance, if the sample size is increased, the probability of committing a Type II error will decrease.
True
*True or False* The critical values will bound the rejection and non-rejection regions for the null hypothesis.
True
*True or False* The probability of making a Type I error and the level of significance are the same.
True
If a hypothesis is rejected at the 0.025 level of significance, it: (***) a) must be rejected at any level. b) must be rejected at the 0.01 level c) must not be rejected at the 0.01 level. d) may or may not be rejected at the 0.01 level.
d) may or may not be rejected at the 0.01 level.
The hypothesis of most interest to the researcher is:
the alternative hypothesis
The probability of a test statistic falling in the rejection region is equal to the value of ____________________.
the significance level (alpha)
The p-value of a test is (2nd definition)
the smallest α (alpha) at which the null hypothesis can be rejected
