Question

       

	Write out example null and alternative hypotheses.	Sampling distribution used by test
One sample test for a mean	H0: mu = 0 H1: mu ≠ 0 (You may choose to write in words)	z-distribution if true standard deviation of population is known t-distribution if true standard deviation of population is unknown
Two sample tests for difference in means
One sample test for a proportion
Two sample tests for difference in proportions
Test for paired difference
Goodness-of- fit chi- squared test
Chi-squared test for independenc e
One-factor ANOVA
Two-factor ANOVA
ANCOVA
Pearson correlation (r)

Simple linear regression (slope)
Mann- Whitney U
Sign test
Wilcoxon signed-rank test
Kruskal- Wallis test
Spearman rank correlation coefficient
Logistic regression
Log-rank test
Cox proportional hazards regression

Explain why each of the confidence intervals were provided their respective labels. Break it up into 7 parts and use a, b, etc., subitem labelin

Answer 1

One sample test for a mean	H0: = 0 H1: ≠ 0	z-distribution if true standard deviation of population is known t-distribution if true standard deviation of population is unknown
Two sample tests for difference in means	Independent Groups: H0: H1:	- Used to compare the means of two independent groups using Z test for means (if true standard deviation of population is known) and t test (if true standard deviation of population is unknown)
One sample test for a proportion		Used to test whether the proportion is equal to a hypothesized value p0 ,using Z test for single proportion
Two sample tests for difference in proportions		Used to compare the proportions of two independent groups using two sample Z test for proportion
Test for paired difference	Paired Groups:	- Used to compare the means of two dependent / paired groups using Paired t test for means di = Difference of observations, is the mean difference
Goodness-of- fit chi- squared test		Used to test whether the observed distribution is same as expected Oi, Ei = Observed and Expected values respectively
Chi-squared test for independence	H0: There is no association between the two variables Ha: There is a significant association between the two variables	- Used to test whether two nominal / categorical variables are associated.
One-factor ANOVA	Ha: Not all means are equal	Used to test the effect of an independent variable (factor) with certain no. levels (n) over a dependent variable i.e. to compare 'n' treatments: If treatment group means equal - it would imply that the dependent variable observations remains the same irrespective of the treatment administered. i.e treatment has no significant effect.
Two-factor ANOVA	H0a: Factor A has no effect H0b: Factor B has no effect H0ab: There is no interaction effect H1a: Factor A has a significant effect H1b: Factor B has a significant effect H1ab: There is a significant interaction effect	Used to test whether two factors (categorical) with certain no. of levels affect the (continuous) dependent variable. And whether their interaction has any effect on dependent variable.
ANCOVA	H0: There is no difference among the adjusted population means H0: There is a significant difference among the adjusted population means	Used to test the effect of an independent variable (factor) with certain no. levels (n) over a dependent variable, controlling for the variable, whose effect we are not interested in i.e. to compare 'n' treatments. It is an extension of ANOVA that provides a way of statistically controlling the (linear) effect of variables we do not want to examine in the study, called covariates, or control variables measured on an interval or ratio scale.
Pearson correlation (r)		Used to test whether a significant linear relationship between two continuous variables,and its the strength and direction. - Pearson's Linear Correlation coefficient

Simple linear regression (slope)	At least one	Used to test whether a significant linear causal relationship between the response (dependent variable) measured in interval / ratio scale and the ith predictor (independent variable) in the regression model
Mann- Whitney U	H0: The distribution of scores for the two groups are equal Ha: The distribution of scores (Mean rank) for the two groups are not equal	Used as a Non - parametric alternative for Independent t test, where, no distributional assumprions is made (unlike in t test where we assume that the population is normally distributed)
Sign test	H0:Medians of the two groups are equal Ha: Medians of the two groups are not equal	Used as a Non - parametric alternative for Paired t test, where, no distributional assumprions is made (unlike in paired t test where we assume that the population is normally distributed)
Wilcoxon signed-rank test	H0:Median is equal to hypothesized value Ha: Median is significantly different from hypothesized value	Used to compare the median against a hypothesized value
Kruskal- Wallis test	H0: The mean ranks of all the n groups are same Ha: The mean ranks of the n groups are not the same	Used as a Non - parametric alternative for One way ANOVA, where, no distributional assumprions is made (unlike in One way ANOVA where we assume that the population is normally distributed and that the variances are homogenous)
Spearman rank correlation coefficient		Used as a Non - parametric alternative for Pearson's correlation coefficient r, to measure the strength and direction of association between two ranked variables where, no assumptions on the linearity of the relationship is made (unlike in Pearson's r where we assume that the relationship is linear)
Logistic regression	At least one	Used to test whether a significant causal relationship between the response (dependent variable) measured in nominal scale and the ith predictor (independent variable) in the regression model. Here, instead of predicting the dependent variable itself (As in linear regression) we predict the probabilities.
Log-rank test	H0: There is no difference in survival between two or more independent groups Ha: There is a significant difference in survival between two or more independent groups	Used to compare the survival distribution of two or more independent groups
Cox proportional hazards regression	At least one	Used to test whether a significant causal relationship between the response Survival time (dependent variable) with one or more predictors in the regression model.