CH 16 Smartbook
A market researcher has 22 persons try two different types of chips. He thinks they will prefer Brand B. What are the appropriate hypotheses for a sign test of this idea?
H0: π ≤ 0.5 H1: π > 0.5
Which of the following are valid hypotheses with a sign test for the median?
Ho: Median = 25 Ho: Median ≤ 25 H1: Median ≠ -25
Which of the following are valid hypotheses with a sign test for the median?
Ho: Median ≥ 110 Ho: Median = - 110
What kind of data can be used with distribution free tests?
Interval scale data. Ordinal scale data. Ratio scale data.
If a pair of observations that is being used for a sign test are assigned a difference of 0, how is this treated in counting the pluses and minuses?
It is not counted.
Which kind of data cannot be used with distribution-free tests?
Nominal scale data.
In doing a Wilcoxon signed-rank test, we find a T of 15. The cutoff value from the table is 17. What is your conclusion?
Reject the null hypothesis, the pairs are from different populations.
Which the of the following statements correctly describe steps of the Wilcoxon signed-rank test?
Sum the ranks for the negative differences and the positive differences, separately. Place absolute differences between pairs in rank order. The smaller sum is the T value.
The median is often used as the measure of central tendency when the population distribution is skewed. How can you conduct a hypothesis test about the value of the median?
Tests of the median require non-parametric tests, such as the sign test.
In a sign test, what happens if two paired observations are the same (that is, they have no difference)?
The difference is 0, and the observations are dropped from the sample.
Suppose you are conducting a sign test (upper tail) with n=13 and no 0 differences. What would be the cutoff level for rejecting the null with α=0.10?
10
What is a "distribution-free" test?
A hypothesis test that does not need to assume anything about the shape of the population distribution.
Which of the following is an accurate description of the Wilcoxon signed rank test?
A test based on the differences in dependent samples, where the normality assumption is not required.
The sign test has only two outcomes, they are independent, and the probabilities for each trial are the same. What distribution do these attributes describe?
Binomial
The Wilcoxon signed-rank test can be used as a non-parametric replacement for the paired t-test to overcome which of the following issues?
The population of difference is not normal. The data is ordinal.
What information is the basis of a sign test?
The sign of a difference between two related observations.
You have learned about many tests for the population mean or proportion, but what can you do to test the median?
The sign test is one of the few tests that can be used to test the median.
Why is it appropriate to use a binomial distribution to calculate the p-value for a sign test?
The sign test meets all the binomial assumptions.
In doing a sign test, assume the significance level is set to α = 0.05. What number of success should we select from the binomial distribution to arrive at the decision rule for an upper tail test?
The smallest number of success, x, such that the probability of having at least x successes is less than 0.05.
The Wilcoxon rank-sum test is a non-parametric test to see whether two independent samples came from equivalent populations. Which of these parametric tests does it replace?
The test of two means. (t-test)
Hypothesis tests designed for nonparametric data require that the data follow:
no particular distribution
