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3) A recent national study found that 27% of college students are raising children. The administration of a local college found that of the 552 newly enrolled students, 165 were raising children. Does this sample give evidence that there is a higher proportion of students attending this college that are parents compared to the nation? Use a significance level of o = 0.05. (8 pts) a) Write the hypotheses using the correct symbols. b) Use the 1-PropZTest command in your calculator to run this hypothesis test. Write the command and the values you entered and then report the test statistic and p-value. c) Write a full conclusion for this test in the context of the problem. d) For any hypothesis test, there is a chance that our conclusion is incorrect. What type of error might we have made in this scenario? 4) Psychology experiments sometimes involve testing the ability of rats to navigate a maze. One researcher needs a maze that will take rats, on average, less than a minute to solve. The data below gives the completion times for this maze for 20 randomly sampled rats. Will the maze fulfill the researcher's time requirement? Use a significance level of a = 0.05. (8 pts) Time (seconds) 48.4 56 2 62.5 52.0 63.8 8 54.5 50.7 43.4 58.3 60.1 55.3 57.6 55.5 5 47.2 54.6 49.9 615 65.2 56.2 a) Write the hypotheses using the correct symbols, b) Use the T-Test command in your calculator to run this hypothesis test. Write the command and the values you entered and then report the test statistic and p-value c) Write a full conclusion for this test in the context of the problem. d) What type of error might we have made in this scenario? 5) The speed limit on local neighborhood road is 25 mph. Even after traffic-calming measures, a resident complains that cars still speed. 250 randomly selected cars were clocked with mean speed 25.55 mph and a standard deviation of 3.618. Does the sample give evidence that cars are speeding on this road? Use a significance level of a = 0.05. (10 pts) a) Write the hypotheses using the correct symbols b) Run the appropriate hypothesis test command in your calculator. Write the command and the values you entered and then report the test statistic and p-value c) Are the results statistically significant? Why or why not? d) Find the appropriate 90% confidence interval using the correct command in your calculator! e) Are the results practically significant? Why or why not