The Central Limit Theorem Central Limit Theorem. Given a population described by any probability distribution having mean µ and finite variance σ2, the sampling distribution of the sample mean X‾\bar{X} computed from random samples of size n from this population will be approximately normal with mean µ (the population mean) and variance σ2/n (the population variance divided by n) when the…
where: SX‾S_{\bar{X}} = the estimate of the standard error of the sample mean, B = the number of resamples drawn from the original sample, θ^b\hat\theta_b = the mean of a resample, and θ‾\bar\theta = the mean across all the resample means.
In hypothesis testing, we test to determine whether a sample statistic is likely to come from a population with the hypothesised value of the population parameter. The Process of Hypothesis Testing A hypothesis is a statement about one or more populations that we test using sample statistics. Stating the Hypotheses Null hypothesis (or null), designated…
The sampling distribution of the mean, when the population standard deviation is unknown, is t-distributed, and when the population standard deviation is known, it is normally distributed, or z-distributed. Since the population standard deviation is unknown in almost all cases, we will focus on the use of a t-distributed test statistic. Test Concerning Differences between Means with Dependent…
Hypotheses concerning the population correlation coefficient may be two- or one-sided, as we have seen in other tests. Let ρ represent the population correlation coefficient. The possible hypotheses are as follows: Two sided: H0: ρ = 0 versus Ha : ρ ≠ 0 One sided (right side): H0: ρ ≤ 0 versus Ha : ρ > 0 One sided (left side): H0: ρ ≥ 0 versus Ha : ρ < 0 Parametric Test of a Correlation…
Describe the variation of the ROAs(Return on Assets) as follows: The variation of X is calculated as follows: Linear regression allows us to test hypotheses about the relationship between two variables by quantifying the strength of the relationship between the two variables and to use one variable to make predictions about the other variable. Estimating…
Four key assumptions to be able to draw valid conclusions from a simple linear regression model:
Analysis of Variance Breaking Down the Sum of Squares Total into Its Components Measures of Goodness of Fit Hypothesis Testing of Individual Regression Coefficients Hypothesis Tests of the Slope Coefficient Hypothesis Tests of the Intercept Hypothesis Tests of Slope When the Independent Variable Is an Indicator Variable Test of Hypotheses: Level of Significance and p-Values
