A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, ʺWhat make of car (U.S., Europe, or Japan) Do you drive?ʺ The responses (number in each category)for a sample of 100 entrepreneurs are Summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs Who drive American, European, and Japanese cars differ. $\begin{array}{ccc} \text { U.S. } & \text { Europe } & \text { Japan } \\ \hline 40 & 35 & 25 \\ \hline \end{array}$ In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a $95 \%$ confidence interval for the multinomial probability associated with the "Europe" response was desired. Which of the following confidence intervals should be used?

A) $( 0.271,0.428 )$ B) $( 0.257,0.443 )$ C) $( 0.265,0.440 )$ D) $( 0.227,0.473 )$ A) $( 0.271,0.428 )$ B) $( 0.257,0.443 )$ C) $( 0.265,0.440 )$ D) $( 0.227,0.473 )$

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: ʺThe government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes.ʺ The possible Responses were ʺagree stronglyʺ, ʺagree somewhatʺ, ʺdisagree somewhatʺ, and ʺdisagree stronglyʺ. The number of Internet users in each category is summarized in the table. $\begin{array}{l|l} \text { RESPONSE } & \text { NUMBER } \\ \hline \text { Agree Strongly } & 60 \\ \text { Agree Somewhat } & 110 \\ \text { Disagree Somewhat } & 80 \\ \text { Disagree Strongly } & 50 \end{array}$ In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a $90 \%$ confidence interval for the multinomial probability associated with the "Disagree Somewhat" response was desired. Which of the following confidence intervals should be used?

A) $( 0.206,0.327 )$ B) $( 0.225,0.309 )$ C) $( 0.216,0.317 )$ D) $( 0.201,0.332 )$ A) $( 0.206,0.327 )$ B) $( 0.225,0.309 )$ C) $( 0.216,0.317 )$ D) $( 0.201,0.332 )$

A professor chose a random sample of 50 recent graduates of an MBA program and recorded the gender of each graduate (M or F)and whether the graduate chose to complete his or her degree requirements by completing a research project (RP)or by taking comprehensive exams (CE). The results are shown below. $\begin{array} { l l l l l } \text { M, CE } & \text { M, RP } & \text { F, RP } & \text { M, CE } & \text { M, CE } \\ \text { F, CE } & \text { F, RP, } & \text { M, CE } & \text { M, RP } & \text { F, RP } \\ \text { F, CE } & \text { M, RP } & \text { F, RP } & \text { F, CE } & \text { M, RP } \\ \text { F, RP } & \text { M, RP } & \text { F, CE } & \text { M, CE } & \text { M, CE } \\ \text { M, RP } & \text { F, CE } & \text { F, RP } & \text { M, CE } & \text { M, CE } \\ \text { F, CE } & \text { M, RP } & \text { F, RP } & \text { M, CE } & \text { M, CE } \\ \text { F, CE } & \text { F, RP, } & \text { M, CE } & \text { M, RP } & \text { F, RP } \\ \text { M, CE } & \text { M, RP } & \text { F, RP } & \text { F, CE } & \text { M, RP } \\ \text { F, RP } & \text { M, RP } & \text { M, CE } & \text { M, CE } & \text { M, CE } \\ \text { M, RP } & \text { F, CE } & \text { F, RP } & \text { M, CE } & \text { F, CE } \end{array}$ a. Create a contingency table for the data. b. Perform a $\chi ^ { 2 }$-test to determine if there is any evidence that gender and choice of research project or comprehensive exams are not independent. Use $\alpha = 0.05$.

a. @#IMG-DLM& b. The rejection region is @#LAT-DLM&; the t

An adverse drug effect (ADE)is an unintended injury caused by prescribed medication. The table summarizes the proximal cause of 95 ADEs that resulted from a dosing error at a Boston hospital. $\begin{array}{lc} \hline \text { WRONG DOSAGE USE } & \text { NUMBER OF ADEs } \\ \hline \text { (1) Lack of knowledge of drug } & 29 \\ \text { (2) Rule violation } & 17 \\ \text { (3) Faulty dose checking } & 13 \\ \text { (4) Slips } & 9 \\ \text { (5) Other } & 27 \\ \hline \text { TOTAL } & 95 \end{array}$ In order to determine whether the true percentages of ADEs in the five "cause" categories differ, a chi-square analysis was conducted. Use the chi-square distribution to determine rejection region when testing at $\alpha = 0.025$.

A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 12.8325$ B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 14.4494$ C) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 11.1433$ D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 9.48773$ A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 12.8325$ B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 14.4494$ C) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 11.1433$ D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 9.48773$

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations. Use $\alpha =$ $0.05$. $\begin{array}{l|ccc} &{\text { Opinion }} \\ \hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\ \text { Republican } & 42 & 20 & 14 \\ \text { Democrat } & 50 & 24 & 18 \\ \text { Independent } & 10 & 16 & 6 \end{array}$ Find the rejection region used to test the claim of independence.

A) $\chi ^ { 2 } > 11.143$ B) $\chi ^ { 2 } > 9.488$ C) $\chi ^ { 2 } > 7.779$ D) $\chi ^ { 2 } > 13.277$ A) $\chi ^ { 2 } > 11.143$ B) $\chi ^ { 2 } > 9.488$ C) $\chi ^ { 2 } > 7.779$ D) $\chi ^ { 2 } > 13.277$