Math 120 Statistics Week 12 Worksheet ZTest for Proportion 2Sample TTest for Two Population Means You may use calculator tests to nd the test statistic and pvalue. Show what test you used and write What you typed in your calculator test to get your answer. Include all ve steps of a hypothesis test: I State the null and alternative hypothesis I State the test statistic I State the pvalue I Decide whether Ho should be rejected I Write a sentence to interpret your results. 1. A report from the NCAA states that 58% of football injuries occur during practice. A head trainer believes that, for schools in her state, this proportion would be different than it is nationally. In her slate, out ofs sample of40 injuries, 40% occurred during practice. Test the trainer's claim at signicance level :1 = 0.05 2. A poll done for Newsweek found that 13% of Americans have reported seeing or sensing the presence ofan angel. A sociologist thinks the reported proportion is too high. She conducts her own survey. Out of l 16 Americans surveyed, only 12 reported having seen or sensed the presence of an angel. Test the sociologists claim at the 5% level of signicance. 3. A medical researcher wishes to compare the mean resting heartrate for adult patients who are professional athletes with other adults. He selects a sample of adults from each population and obtains the following sample statistics. Conduct a hypothesis test at the 1% level of significance to determine if the resting heartrate of professional athletes is less than the resting heartrate of other adults. Sample Mean Sample Size Sample Standard Deviation Professional Athletes 68 20 7.2 Other Adults 72 35 7.84. A manufacturing company builds a machine that is designed to glue two component parts together. The engineers hoped their new design made the bond stronger when compared to an old design. To test this= they used machines using the old design and using the new design to glue :1 sample of component parts. Then they used another machine to break the bond. The shear force (in kg) needed to separate the parts was recorded. A higher level of force indicates that the glue is stronger since it takes more force to tear the components apart. Test the hypothesis that the new method of gluing component parts is more effective than the old method. What can be concluded at sigiieance level a = 0.01? Original Design New Ensign 171 = 30. 383 51 = 9.444 n] = 30 2 = 54.488 51 = 13. 544- 112= 35 18.779 31.479 23.632 23.179 29.801 56.950 50.464 54.522 42.411 59.693 42.910 35.153 36.197 34.518 46.357 53.795 76.612 41.367 36.696 53.775 31253 49.260 19459 21179 32432 43.908 56.336 74.117 45.904 59.647 421319 20412 19550 16.60]. 26.807 51.165 62.051 51.392 69.354 49.169 39351 36.423 3&0\" 20094 21750 54.975 41.141 37.830 35.698 85.547 19232 20311 23531 30399 45394 41.594 33.475 69.445 66.179 69.173 38.964 49.305 53.025 73.663 37.240