Student body leaders at a college want to conduct a survey to determine the proportion of students who favor a proposed honor code. 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 5% using a 95% confidence interval. What is the sample size they need to ensure above specifications in their estimation?  

Let A and B be events such that  Then P( A and B) is given by:

For each of the below statements, state if it is true or false. 

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:

Students in an introductory statistics class participate in a mid-semester survey. They were asked whether having quizzes better prepare them for the midterms. Their opinion of quizzes were coded as “0” if the answer is No, “1” if the answer is somewhat helpful, “2” if the answer is yes. This variable is:  

A study wants to explore if the average life time of a certain brand of a watch battery has increased over the past ten years. Suppose that a survey was done in 2013 on the average life time of that brand of watch battery.  The same survey was done again in 2023.  What is the correct interpretation of the probability of making a Type II error in the context of this problem?

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 sociological study is planed to conduct in a small town to estimate the proportion of households with at least one senior (over 65 years old) individual. They want to estimate the true proportion with a margin of error no larger than 0.04 using a 95% confidence interval. How many households should be sampled in order to ensure the above specifications in their estimation? 

Using the following five-number summary, indicate whether each statement below is true or false.  Minimum Q1 Median Q3 Maximum 20 35.6 52 72 99  

What do Phylis Schlafly and Anita Bryant have in common?