# Chi square test of independence and Z test

6. A researcher is interested in studying the relationship between certain driving habits and type of vehicle. He hypothesizes that signaling behavior will be different for drivers of trucks and cars. The data from observations made while driving are given below. Calculate the two-variable Chi-square test. State the null hypothesis, alternate hypothesis, find the Chi-square critical value (for alpha of 0.05), and present the statistical decision.

Vehicle Type

Signal Cars Trucks

Yes 190 267

No 183 209

7. The national graduate rate for state police academies is 90%. In the latest graduating class of Big State Police Academy, 240 of 300 cadets graduated. Teh state governor has begun an inquiry into the low rate of graduation. But, first, he has asked you to determine if the difference in rates is significant or due to chance. Use an alpha of 0.01 for a two-tail test of significance.

8. A prison has been selected for study by a state regulatory agency that monitors job placement training and success. Nationally, 35% of those released on parole are still employed one year after release. A sample of 300 parolees indicated that 126 are still employed after one year. Is this prison's job training program better, worse, or no different from the national average? Use a two-tailed test with an alpha of 0.05.

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#### Solution Summary

The solution gives the details of chi-square test of independence and testing of equality of population proportion. Null hypothesis, alternative hypothesis, critical value and p value are given.