Question

When should I use the Sign Test (single variable)?

Remember that some tests, such as chi squared, can be used under various circumstances. The goal of the test changes based on the situation. Pay attention to the specific conditions noted in parenthesis to ensure you are picking the correct goal.

	A.	Test to see if the frequency data from a population fit a discrete probability distribution.
	B.	Compare categorical frequency data with an expected population proportion. No difference between observed and expected proportions is used as the null hypothesis.
	C.	Compare two treatment groups when a normal distribution cannot be assumed.
	D.	More than two treatment groups where a normal distribution can be assumed.
	E.	Compare two treatments consisting of paired data where a normal distribution can be assumed.
	F.	Test the fit of the normal distribution to the data set.
	G.	Compare two treatment groups consisting of paired data when the data do not fit the normal distribution.
	H.	Compare two treatment groups of independent samples where the data meet the assumption that the data fit the normal distribution.
	I.	Test to compare frequency data to a specific population model
	J.	Compare more than two treatment groups when a normal distribution cannot be met.
	K.	Compares numerical data to a known mean. The null hypothesis is that the mean of the data equals the known mean.
	L.	Test if the median of a data set equals a null hypothesized value when the distribution of the data does not meet the assumption of normalacy.
	M.	Compare two treatment groups consisting of independent samples with a normal distribution AND unequal variance.

When should I use theX² Goodness-of-fit test (numerical data to compare with discrete probability distribution)?

Remember that some tests, such as chi squared, can be used under various circumstances. The goal of the test changes based on the situation. Pay attention to the specific conditions noted in parenthesis to ensure you are picking the correct goal.

	A.	Test the fit of the normal distribution to the data set.
	B.	Compare two treatment groups consisting of paired data when the data do not fit the normal distribution.
	C.	Compare more than two treatment groups when a normal distribution cannot be met.
	D.	Test to see if the frequency data from a population fit a discrete probability distribution.
	E.	Compares numerical data to a known mean. The null hypothesis is that the mean of the data equals the known mean.
	F.	Test if the median of a data set equals a null hypothesized value when the distribution of the data does not meet the assumption of normalacy.
	G.	Compare two treatment groups when a normal distribution cannot be assumed.
	H.	Compare categorical frequency data with an expected population proportion. No difference between observed and expected proportions is used as the null hypothesis.
	I.	Compare two treatments consisting of paired data where a normal distribution can be assumed.
	J.	Test to compare frequency data to a specific population model
	K.	Compare two treatment groups of independent samples where the data meet the assumption that the data fit the normal distribution.
	L.	Compare two treatment groups consisting of independent samples with a normal distribution AND unequal variance.
	M.	More than two treatment groups where a normal distribution can be assumed.

Answer 1

When we sign test .

Sign test is an non parametric test in this test we do not assume that the data is normally distributed . There are two type of this test 1)single variable and 2)paired variable.

Now in single variable we do not assume the data is normal and we testing hypothesis on the median rather than mean .So the in given example situation L is the correct one .that is test if the median of the data set equals a null hypothesis value when distribution of the data does not meet the assumption of normalcy.

Chi square test ..

The goodness of fit test for discrete distribution is basically

We try to fit some probability distribution since there are several probability distribution, which distribution will fit properly may be a question of interest. In such cases we want to test the appropriateness of the fit .so in this case we Ho : Fitting the discrete probability distribution to given data is good .Since given data is numerical that's why situation is D is correct.That is test to see if the frequency data from a population fit a discrete probability distribution.