DP Mathematics HL Questionbank
7.7
Description
[N/A]Directly related questions
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 16M.3sp.hl.TZ0.2c: Explain why the equation of the regression line of \(y\) on \(x\) should not be used to predict...
- 16M.3sp.hl.TZ0.2b: (i) Determine the \(p\)-value. (ii) State your conclusion at the 5% significance level.
- 16M.3sp.hl.TZ0.2a: State suitable hypotheses to investigate whether or not \(X\), \(Y\) are independent.
- 16N.3sp.hl.TZ0.1c: Using a suitable regression line, find an estimate for his score on Exam 2, giving your answer to...
- 16N.3sp.hl.TZ0.1b: (i) State the distribution of the test statistic (including any parameters). (ii) Find...
- 16N.3sp.hl.TZ0.1a: For these data find the product moment correlation coefficient, \(r\).
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17M.3sp.hl.TZ0.5c: The teacher then asks Anne for the values of the \(t\)-statistic and the product moment...
- 17M.3sp.hl.TZ0.5b: State, in context, what conclusion should be drawn from this \(p\)-value.
- 17M.3sp.hl.TZ0.5a: State suitable hypotheses for this investigation.
- 15N.3sp.hl.TZ0.2c: If the moisture content of a beam is found to be \(9.5\), use the appropriate regression line to...
- 15N.3sp.hl.TZ0.2a: Determine the product moment correlation coefficient for these data.
- SPNone.3sp.hl.TZ0.4c: George obtained a mark of 63 on Paper 1 but was unable to sit Paper 2 because of illness. Predict...
- SPNone.3sp.hl.TZ0.4d: Another class of 16 students sat examinations in Physics and Chemistry and the product moment...
- SPNone.3sp.hl.TZ0.4a: State suitable hypotheses.
- SPNone.3sp.hl.TZ0.4b: The marks obtained by the 12 students who sat both papers are given in the following...
- 14M.3sp.hl.TZ0.2: The following table gives the average yield of olives per tree, in kg, and the rainfall, in cm,...
- 14N.3sp.hl.TZ0.3a: If \(X\) and \(Y\) are two random variables such that \({\text{E}}(X) = {\mu _X}\) and...
- 14N.3sp.hl.TZ0.3b: In a particular company, it is claimed that the distance travelled by employees to work is...
Sub sections and their related questions
Introduction to bivariate distributions.
- SPNone.3sp.hl.TZ0.4a: State suitable hypotheses.
- SPNone.3sp.hl.TZ0.4b: The marks obtained by the 12 students who sat both papers are given in the following...
- SPNone.3sp.hl.TZ0.4c: George obtained a mark of 63 on Paper 1 but was unable to sit Paper 2 because of illness. Predict...
- SPNone.3sp.hl.TZ0.4d: Another class of 16 students sat examinations in Physics and Chemistry and the product moment...
- 14M.3sp.hl.TZ0.2: The following table gives the average yield of olives per tree, in kg, and the rainfall, in cm,...
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Covariance and (population) product moment correlation coefficient \(\rho \).
- 14N.3sp.hl.TZ0.3a: If \(X\) and \(Y\) are two random variables such that \({\text{E}}(X) = {\mu _X}\) and...
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Proof that \(\rho = 0\) in the case of independence and \( \pm 1\) in the case of a linear relationship between \(X\) and \(Y\).
- 14N.3sp.hl.TZ0.3a: If \(X\) and \(Y\) are two random variables such that \({\text{E}}(X) = {\mu _X}\) and...
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Definition of the (sample) product moment correlation coefficient \(R\) in terms of n paired observations on \(X\) and \(Y\). Its application to the estimation of \(\rho \).
- 15N.3sp.hl.TZ0.2a: Determine the product moment correlation coefficient for these data.
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Informal interpretation of \(r\), the observed value of \(R\). Scatter diagrams.
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Topics based on the assumption of bivariate normality: use of the \(t\)-statistic to test the null hypothesis \(\rho = 0\) .
- 14N.3sp.hl.TZ0.3b: In a particular company, it is claimed that the distance travelled by employees to work is...
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Topics based on the assumption of bivariate normality: knowledge of the facts that the regression of \(X\) on \(Y\) (\({E\left. {\left( X \right)} \right|Y = y}\)) and \(Y\) on \(X\) (\({E\left. {\left( Y \right)} \right|X = x}\)) are linear.
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Topics based on the assumption of bivariate normality: least-squares estimates of these regression lines (proof not required).
- 15N.3sp.hl.TZ0.2c: If the moisture content of a beam is found to be \(9.5\), use the appropriate regression line to...
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
Topics based on the assumption of bivariate normality: the use of these regression lines to predict the value of one of the variables given the value of the other.
- 15N.3sp.hl.TZ0.2c: If the moisture content of a beam is found to be \(9.5\), use the appropriate regression line to...
- 17N.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not \(U\), \(V\) are independent.
- 17N.3sp.hl.TZ0.4b: Find the least value of \(|r|\) for which the test concludes that \(\rho \ne 0\).
- 18M.3sp.hl.TZ0.4a: State suitable hypotheses to investigate whether or not a negative linear association exists...
- 18M.3sp.hl.TZ0.4b.i: Determine the p-value.
- 18M.3sp.hl.TZ0.4b.ii: State your conclusion at the 1 % significance level.
- 18M.3sp.hl.TZ0.4c.i: Show that Cov(U, V) = E(UV) − E(U)E(V).
- 18M.3sp.hl.TZ0.4c.ii: Hence show that if U, V are independent random variables then the population product moment...
