WRITE A PAPER ON THE STATISTICS/ INTRODUCTORY STATISTICS Clearly label each part and each section within each part. SECTION ONE Question 1 4.3 Sophia who took the Graduate Record Examination (GRE) scored 160 on the Ver- bal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal. . Consider Exercise 4.3 above , on page 142 (OpenIntro Statistics ,Fourth Edition ,David Diez ). Focus on the distribution of the verbal part of the GRE. Answer the following question Show all the details in your calculations. (1) What proportion of students scored below 157? (2) What proportion of students scored above 147? (3) What proportion of students scored between 149 and 170? (4) Obtain the first quartile of this distribution, and interpret the result. (5) Obtain the third quartile of this distribution, and interpret the result. (6) Calculate the inter-quartile range (IQR), and interpret the result. (7) Obtain the 85th percentile of this distribution, and interpret the result. Question 2 It is estimated that 34% of all college students live on campus. You select a random sample of 30 college students. Answer the following question and be sure to c show associated graphs pattern, except for part (6): (1) What is the probability that exactly ten (10) students live on campus? (2) What is the probability that at most twelve (12) students live on campus? (3) What is the probability that at least eight (8) students live on campus? (4) What is the probability that more than eight (8) students live on campus? Hint: What is the needed number of successes here? (5) Determine the 65th percentile in this distribution, and interpret the result. (6) Calculate the mean and standard deviation of this distribution, and interpret the results. SECTION II. Question 3 Part 1 Define the following terms: (1) Hypothesis test (2) Null and alternative hypotheses (3) p-value (4) Significance (alpha) level (5) Chi-square test of independence Discuss the relationship between confidence intervals and hypothesis testing Part 2 Using the attached file Focus on the variable “vaccinated.” (1) You need to test whether the proportion of individuals who received flu vaccine is significantly different from 60%. State the research question. (2) State both hypotheses. (3) Copy and paste the complete results of the hypothesis test and associated 95% confidence interval. Identify the p-value, and confidence limits. (4) State your decision regarding the p-value, and be sure to answer the research question. (5) Assess the strength of your conclusion using the p-value. (6) Specify the 95% confidence interval for the population proportion and interpret the result. (7) How does the result in (6) relate to the conclusion in (4) and (5)? Be specific and succinct. Part 3 Using the same data set, you need to examine possible association between “vaccinated” and “gender.” In other words, you need to see whether gender somehow affects the rate of vaccination. (1) State the research question. (2) State both hypotheses. (3) Perform an appropriate test of association. Copy and paste the complete results, including the contingency table showing marginal, joint, and conditional probabilities. (4) What proportion of females got vaccinated? (5) What proportion of non-vaccinated individuals are male? (6) Report the results of the hypothesis test, and state your decision regarding the null hypothesis. (7) Answer the research question. (8) Assess the strength of your conclusion using the p-value. (9) Provide the Cramer’s V (or Phi-Coefficient) for this test, and assess the strength of association between the two variables. (10) Provide the bar graph for the variable “vaccinated” when split by “gender.” Briefly describe what you see and how does this graph support your decisions in (6) and (9).