Statistics for management, tests summary, assumptions, quantitative variable, normal distribution, alternate, ample mean, population mean
Assumptions: quantitative variable, normal distribution.
Null: Sample mean is same as the population mean.
Alternate: Sample mean is not same as the population mean. To compare the mean of two given samples.
Assumptions: normal distribution of the sample.
There are three versions of t-test :
1. Independent sample t-test which compares mean for two groups;
2. Paired sample t-test which compares means from the same group at different times;
3. One sample t-test which tests the mean of a single group against a known mean.
[...] —> Two-tailed, upper or lower tailed-test. C. F-test (known parameters) To compare two populations' variances. Hypothesis: H0: σA²=σB²=0 H1: σA2> σB² Test statistic: F = SB1²/ SB2² Decision rule: reject H0 if FnA-1, nb-1; a —> Upper-tailed test. II. Hypothesis testing in Multiple Linear Regression A. T-test Hypothesis: H0: B1=0 H1: Test statistic: tb1 = b1/Sb1 Decision rule: reject H0 if t > tn-k-1;a/2. If we reject the null, —> significant. —> Two-tailed, upper or lower tailed-test. B. Confidence intervals b1 ± tn-k-1;a/2Sb1 C. [...]
[...] OLS assumptions: We assume a linear model with respect to parameters. The error terms, εi, are independent of the x values. The error terms are random variables with mean 0 and constant variance, σ² the error variance), where ε comprises all factors that influence the values of Y beyond the influence of X. Hence, E(ε)=0 means that the average influence of all these factors is zero. Constancy of the variance refereed to as homoskedasticity. When it does not hold, the error term is said to be heteroskedasticity. [...]
[...] Statistics for Management – Tests Summary I. Basic testing A. Z-test (known parameters) Assumptions: quantitative variable, normal distribution. Null: Sample mean is same as the population mean. Alternate: Sample mean is not same as the population mean. Test statistic: where sample mean = population mean σ / √n = population standard deviation Decision rule: reject H0 if Z > Za. —> Upper tail or lower tail. B. T-test (unknown parameters) To compare the mean of two given samples. Assumptions: normal distribution of the sample. [...]
[...] —> Always right-tailed. —> MSD table. E. Logarithmic transformation • Level-level model y = 52 + 2.3 x A unit change in the advertising expenditures (in thousands increases sales by 2.3 thousands △ y = B1*△ x • Log-log model (constant elasticity model) log(y) = 48 + 1.8 log(x) A % increase in the advertising expenditures implies a increase in sales. y = B1*%△ x • Log-level model Y is transformed while x isn't. log(y) = 36 + 0.03 x A unit change in advertising expenditures (in thousands increase sales by 3%. [...]
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