Week 11 to Week 15 Statistics

(HW11) x̅1 - x̅2 is an unbiased statistic that is used to estimate μ1 − μ2.

True

(HW12) A chi-squared goodness-of-fit can be used to test hypotheses about the proportion of the population falling into each of the possible categories.

True

(HW12) The chi-squared test statistic χ 2 measures the extent to which the observed cell counts differ from those expected when H0 is true.

True

(HW13) A standardized residual plot with spread increasing from left to right suggests that the variance of y is not the same at each x value.

True

(HW13) In the simple linear regression model, the point estimate and the point prediction are identical for a particular value of x.

True

(HW13) In the simple linear regression model, the randomness of e implies that y itself is subject to uncertainty.

True

(HW13) The mean value of the statistic b is β.

True

(HW10) If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

False

(HW10) The power of a test is the probability of failing to reject the null hypothesis.

False

(HW10) The statement s2 = 100 is a statistical hypothesis.

False

(HW11) For two independent samples, σx̅1¯ - x̅2 = sqrt((σ1^2/n1)-(σ2^2/n2.

False

(HW11) The number of degrees of freedom of the two-sample t test are the same as the degrees of freedom for the paired t test statistic.

False

(HW11) p ^ 1 − p ^ 2 is a biased estimator of p1 − p2, where p1 and p2 are population proportions and p ^ 1 and p ^ 2 are the corresponding sample proportions.

False

(HW12) For a sample size n, there are n − 1 degrees of freedom associated with the goodness-of-fit test statistic χ 2.

False

(HW12) For the chi-squared goodness-of-fit chi-squared test, the associated P-value is the area under the appropriate chi-squared curve to the left of the calculated value of χ 2.

False

(HW12) In order to decide whether the observed data is compatible with the null hypothesis, the observed cell counts are compared to the cell counts that would be expected when the alternative hypothesis is true.

False

(HW12) The chi-squared test statistic for testing independence in a two-way tables has rc − 1 degrees of freedom, where r is the number of rows and c is the number of columns.

False

(HW12) The expected cell count for the row a and column b entry in a bivariate contingency table is equal to the product of the row a and column b marginal totals.

False

(HW13) In the simple linear regression model, σe (or simply, σ), the standard deviation of e, depends on the value of x.

False

(HW13) The expected change in the value of y for one unit change in x is α.

False

(HW13) The simple linear regression model is a deterministic model.

False

(HW14) The fundamental identity for a single-factor ANOVA is MSTo = MSTr + MSE.

False

(HW14) The objective of a single-factor analysis of variance for k populations is to test the equality of the k population variances.

False

(HW14) The test statistic for testing the equality of population means in a single-factor ANOVA is SSTr/SSE

False

(HW14) When the discrepancies between the values of the 's in a single-factor ANOVA can be attributed to sampling variability, the H0 : μ1 = μ2 = ... = μk should be rejected.

False

(HW14) When using the Tukey-Kramer multiple comparison procedure, if the confidence interval for μ1 − μ2 contains 0 then μ1 and μ2 are declared to be significantly different.

False

(HW10) A type II error is made by failing to reject a false null hypothesis.

True

(HW10) All other things being equal, choosing a smaller value of α will increase the probability of making a type II error.

True

(HW10) It is customary to say that the result of a hypothesis test is statistically significant when the p-value is smaller than α.

True

(HW10) Small p-values indicate that the observed sample is inconsistent with the null hypothesis.

True

(HW10) The choice of the alternative hypothesis depends on the objectives of the study.

True

(HW10) The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

True

(HW11) The number of degrees of freedom used in the two-sample t test for independent samples are the same as the degrees of freedom used in the construction of a confidence interval for μ1 − μ2.

True

(HW11) Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.

True

(HW12) The formulas for the expected cell counts and degrees of freedom for the chi-squared test used to test whether the true category proportions of two or more populations are computed in the same way as for the chi-squared test of the independence of two variables.

True

(HW13) In the simple linear regression model, α and β are fixed numbers that are usually unknown.

True

(HW13) In the simple linear regression, the standard deviation of y is the same as the standard deviation of the random deviation e.

True

(HW13) The general form of additive probabilistic model is y = deterministic function + random deviation.

True

(HW13) The standard deviation of a + bx* grows larger the farther x* is from .

True

(HW14) As long as the other assumptions are plausible, the F test for testing the equality of population means in an ANOVA can be safely used when the largest sample standard deviation is no more than twice the smallest standard deviation.

True

(HW14) SSE measures the within-sample variability.

True

(HW14) The P-value associated with the calculated F value in an ANOVA is the area to the right of the calculated value under an F distribution curve.

True