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At a university, 19% of students are graduate students. 32% of students like horror movies, and 7% of students are graduate students and like horror movies. What is the probability that a randomly selected student is either a graduate student or likes horror movies? [fill1] If a randomly selected student like horror movies, what is the probability that it is a graduate student? [fill2]

State if each of the below statement about simple linear regression and correlation is either true or false.  

Researchers are studying the effect of energy drinks at six different caffeine doses on student alertness. Eight students are randomly assigned to each of the six dose groups. After consuming the energy drink for a set period, their alertness levels are measured using a standardized test. The goal of the study is to determine whether there is a significant difference in student alertness based on the caffeine dose. ANOVA is used to test this. What are the treatment degrees of freedom? [fill1]  What is the following: concluding that the true mean alertness level is not different for these caffeine doses when it is significantly different for at least one caffeine dose? [fill2]   

For the test of whether the true mean monthly rent for Penn State graduate students is greater than $1000,  

The p value for testing

Please note that this question consists of six parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A company wants to test if the average number of tasks completed per day by employees is different from 20. Management randomly selects 12 employees and records the number of tasks completed in a day. For this sample the mean is 21.67 tasks and standard deviation is 2.69 tasks. Set up appropriate null and alternative hypotheses for testing the question posed by the company. Are the conditions to carry out the above stated test are satisfied? If the conditions are satisfied, explain how they were satisfied for this problem rather than simply giving a “yes” or “no” answer. Calculate the test statistic. Show your calculations. Find the rejection region for the test defined in part 1. Use 5% significance level. It is not sufficient to provide just the critical value. Clearly state the rejection region. Write the final conclusion in the context of the problem. Based on the decision you made in part 5, which error: type I or type II is possible? Explain. 

Please note that this question consists of three parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  In a college town, there is a central location where people can drop-off miscellaneous plastics that were not collected in regular weekly pick-ups. The authorities want to study the true proportion of households using the drop-off location for plastic recycling. They have taken a random sample of 120 households and asked them if they use drop-off facility. Of the sampled households, 45 said they use the drop-off bins.  Find a 95% confidence interval for the true proportion of households using the drop-off location for plastic recycling. Interpret the above calculated interval in the context of the problem. The authorities believe about 35% of the households in the town are using the drop-off location for plastic recycling. Based on the interval in part 1, are the authorities correct? Explain.

The administration of a large university is planing on increasing the student fees with the intention of using majority of the funds towards renovations in the football stadium. In a random sample of 60 students, 38 support of the idea. A 90% confidence interval for the true proportion of students who oppose this idea is 

A sample of 15 subjects is collected for the test of

A private courier company claims that their average delivery time within a major city is under 90 minutes. A customer protection agency is investigating the complaints from customers about long delivery times. What are the correct hypotheses to answer the agency’s question?