Statistical Analysis PaperQ1: In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 74 points. The student who took the make-up the following day scored 64 points on the exam. What is the new average? Does the new student’s score increase or decrease the average score? Clearly show your calculations and any interpretations.Q2: The smallpox data set provides a sample of 6,224 individuals from the year 1721 who were exposed to smallpox in Boston. Doctors at the time believed that inoculation, which involves exposing a person to the disease in a controlled form, could reduce the likelihood of death.Each case represents one person with two variables: inoculated and result. The variable inoculated takes two levels: yes or no, indicating whether the person was inoculated or not. The variable result has outcomes lived or died. These data are summarized in the following table.Find the probability that a randomly selected person who was not inoculated died from smallpox. Then, determine the probability that an inoculated person died from smallpox. Compare your results for both. Clearly show your calculations and any interpretations.Q 3: To evaluate whether college-educated adults who get the question about infant vaccination correct is different from 33.3%, the answers of 50 college-educated adults were compared. Of these 50 adults, 24% of respondents got the question correct that 80% of 1 year olds have been vaccinated against some disease.Check conditions whether it is reasonable to construct a confidence interval for p using the sample data, and if so, construct a 95% confidence interval. Show your calculations and interpretations.Q 4: The data were obtained for times of sleep for randomly selected adult subjects included in the National Health and Nutrition Examination Study, and those times (hours) are listed below.4 8 4 4 8 6 9 7 7 10 7 8Here are the unrounded statistics for this sample: n = 12, = 6.83333333 hours, s = 1.99240984 hours.A common recommendation is that adults should sleep between 7 hours and 9 hours each night. Test the claim that the mean amount of sleep for adults is less than 7 hours.Q 5:The graph shows the relationship between hourly wage (in US dollars) and tenure (in numbers of years).a) Describe the relationship between hourly wage and tenure (is it positive or negative?). Comment on the strength of the relationship based on the graph.b) See the Stata results given below. Write down the regression equation for your model based on the results. Interpret the slope and intercept in context. Write your comments encompassing the necessary details.

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