Problem 20
Gender of Shoppers Twenty shoppers are in a checkout line at a grocery store. At \(\alpha=0.05,\) test for randomness of their gender: male \((\mathrm{M})\) or female \((\mathrm{F})\). The data are shown here. $$\begin{array}{c}\text{F M M F F M F M M F}\\\ \text{F M M M F F F F F M}\end{array}$$
Problem 25
Gender of Patients at a Medical Center The gender of the patients at a medical center is recorded. Test the claim at \(\alpha=0.05\) that they are admitted at random. $$ \begin{array}{llllllllll} \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{F} \\ \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{F} & \mathrm{M} \\ \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} \\ \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{M} \end{array} $$
Problem 26
Speeding Tickets A police chief records the gender of the drivers who receive speeding tickets. Test the claim at \(\alpha=0.05\) that the gender of the ticketed drivers is random. $$ \begin{array}{llllllllll} \text { M } & \text { M } & \text { M } & \text { F } & \text { F } & \text { M } & \text { F } & \text { M } & \text { F } & \text { M } \\ \text { M } & \text { F } & \text { M } & \text { M } & \text { M } & \text { F } & \text { M } & \text { M } & \text { F } & \text { F } \\ \text { F } & \text { M } & \text { M } & \text { F } & \text { M } & \text { M } & \text { F } & \text { M } & \text { M } & \text { M } \\ \text { M } & \text { M } & \text { F } & \text { M } & \text { F } & \text { F } & \text { F } & \text { M } & \text { M } & \text { M } \\ \text { F } & \text { F } & \text { M } & \text { F } & \text { F } & \text { F } & \text { M } & \text { M } & \text { M } & \text { M } \end{array} $$
Problem 27
Accidents or Illnesses The people who went to the emergency room at a local hospital were treated for an accident (A) or illness (I). Test the claim \(\alpha=0.10\) that the reason given occurred at random. $$ \begin{array}{llllllllll} \text { I } & \text { A } & \text { I } & \text { A } & \text { A } & \text { A } & \text { A } & \text { A } & \text { A } & \text { I } \\ \text { A } & \text { I } & \text { I } & \text { A } & \text { A } & \text { I } & \text { I } & \text { A } & \text { A } & \text { A } \\ \text { A } & \text { I } & \text { A } & \text { I } & \text { A } & \text { A } & \text { A } & \text { I } & \text { I } & \text { A } \\ \text { A } & \text { I } & \text { I } & \text { A } & \text { A } & \text { I } & \text { A } & \text { I } & \text { A } & \text { I } \\ \text { A } & \text { I } & \text { A } & \text { A } & \text { I } & \text { I } & \text { A } & \text { A } & \text { A } & \text { I } \\ \text { I } & \text { A } & \text { I } & \text { A } & \text { A } & \text { I } & \text { I } & \text { A } & \text { A } & \text { A } \end{array} $$
Problem 29
When \(n \geq 30,\) the formula \(r=\frac{\pm z}{\sqrt{n-1}}\) can be used to find the critical values for the rank correlation coefficient. For example, if \(n=40\) and \(\alpha=0.05\) for a two-tailed test, $$ r=\frac{\pm 1.96}{\sqrt{40-1}}=\pm 0.314 $$ Hence, any \(r_{s}\) greater than or equal to +0.314 or less than or equal to -0.314 is significant. Find the critical \(r\) value for each (assume that the test is two-tailed). $$ n=50, \alpha=0.05 $$
Problem 32
When \(n \geq 30,\) the formula \(r=\frac{\pm z}{\sqrt{n-1}}\) can be used to find the critical values for the rank correlation coefficient. For example, if \(n=40\) and \(\alpha=0.05\) for a two-tailed test, $$ r=\frac{\pm 1.96}{\sqrt{40-1}}=\pm 0.314 $$ Hence, any \(r_{s}\) greater than or equal to +0.314 or less than or equal to -0.314 is significant. Find the critical \(r\) value for each (assume that the test is two-tailed). $$ n=60, \alpha=0.10 $$
