Here are copies of Z-table and T-table.  Z table.pdf T_table.pdf  

Please note that this question consists of five parts. Show all your work. Just giving the answer without showing work may result in zero for the question.  Data from a simple random sample of 121 Penn State seniors were collected. As a part of the study, they were asked below two questions: What is your current GPA? Are you planning on applying to graduate school? For the sampled 121 students, the average GPA is 3.6 and the standard deviation is 0.36. Find a 95% confidence interval for the average GPA of Penn State seniors.   A recent study claims that the average undergraduate GPA in U.S. universities is about 3.4. Based on your calculation in part 1, are Penn State seniors doing better in terms of their GPA? In the sample of 121 students, 18 said they plan on applying to graduate school. Find a 95% confidence interval for the proportion of Penn State seniors who plan on going to graduate school.  What conditions need to be satisfied in order for you to calculate the confidence interval in part 3? Are they satisfied? Rather than constructing a confidence interval, I decided to carryout the below hypothesis test.  Formulated hypothesis is:

For each of the following, select the correct answer from the dropdown menu.  If A and B are mutually exclusive events then P(A) = P(B) = 0.5 This is a statement.  If A and B are independent events, then

Please note that this question consists of three parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  Fifty six percent of the undergraduate students in a college lives off-campus, 68% have a car, and 49% live off-campus and have a car. We randomly select an undergraduate student. Are the events “living off-campus” and “have a car” mutually exclusive? Explain your answer.   What is the probability that the student neither lives off-campus nor have a car? What is the probability that he/she has a car, if he/she lives off-campus?

Please note that this question consists of six parts. You need to show all mathematical calculations to get the final answer. Just giving the answer without showing work may result in zero for the question. Are the means for the final exams same for all statistics class delivery types? Data on the scores on final exams from several randomly selected classes that used the different delivery types – Face-to-Face, Hybrid, Online are obtained. Purpose of the study was to determine whether the average scores on final exams would be the same for all three different delivery types.  Research group who conducts the study have decided to use One-way ANOVA to compare the mean scores on final exams. They need help from a statistician to interpret the results. Use provided partial output to answer the following questions. Write down the null and alternative hypotheses for testing whether or not the average scores on final exams would be same for all three different delivery types. Define the parameters and use those defined parameters when you set up null and alternative hypotheses. Compute the degrees of freedom missing in the ANOVA output (i.e. error degrees of freedom) Compute the sum of squares missing in the table (i.e.: Sum of square treatment)  Compute the F-value missing in the ANOVA output. At a 5% significant level is there sufficient evidence to claim that the true average scores on final exams are different for at least one of the delivery types. Explain your answer. The output for Tukey pairwise comparisons is given below. Based on the output Is the average final exam scores for Face-to-Face and Hybrid are significantly different? Explain your answer. Which class type seems to have the highest average final exam score?      

A certain university is divided into six colleges, with most students graduating from four of these colleges. The following bar chart gives the distribution of the percent graduating from the four most popular colleges in 2019. The percent of students graduating from either engineering or business is:      

A student organization wanted to see who lives on-campus and who lives off-campus. They selected 100 students at random from each class, freshmen through seniors. The sampling technique being used is:  

Student Government Association (SGA)  at a college wants to conduct a survey to determine the proportion of students who voted for election of of the SGA President. Since interviewing all the students is not feasible due to practical reasons, they want to determine the sample size (number of students to be interviewed) needed to estimate the true proportion with a margin of error no larger than .1 using a 98% confidence interval. What is the sample size they need to ensure above specifications in their estimation? Choose the appropriate z-multiplier for the calculation from the below provided values.    

“We think that, by using its public school system to encourage recitation of the Regents’ prayer, the State of New York has adopted a practice wholly inconsistent with the Establishment Clause…For this reason, petitioners argue, the State’s use of the Regents’ prayer in its public school system breaches the constitutional wall of separation between Church and State. We agree with that contention, since we think that the constitutional prohibition against laws respecting an establishment of religion must at least mean that, in this country, it is no part of the business of government to compose official prayers for any group of the American people to recite as a part of a religious program carried on by government.” Engel v. Vitale, 370 U.S. 421, 424-25 (1962)   What group or organization would have worked hardest in the 1980s to see a reversal of this Supreme Court decision?  

Which of the following is NOT a role of the Environmental Protection Agency?