Part 2 (50 points). How can we use this sample to make inferences? Explain and narrate all parts as directed. A. Explain how this sample meets the requirements of using a t distribution. Mention the degrees of freedom. B. Estimate a 95% confidence interval for the population mean using your data as a sample. Tell what calculator or Stat Crunch command you used. Explain what this interval means. What is the margin of error? Use the point estimate and the margin of error to write a sentence that summarizes this result. C. The average math PAT score is 512 and the average verbal score is 510. Use the appropriate null hypothesis for your set of data. Perform a two-tailed p-value and a classical hypothesis test. Show all five steps for p-value test and the additional steps for the classical test. Use your data as the sample at the = .05 level. Does your result mesh with the result of the confidence interval in part B? Explain how. D. Split the females and males in your sample into two columns. (See StatCrunch/Data/Arrange/Split). Create two boxplots of the comparable measurement of the opposite gender using the same scale. Report the mean and standard deviation for each gender. Comment on the differences you observe (at least a paragraph) between the genders from what you observe in the five-number summaries of the boxplots and the mean and standard deviation. Which gender does better in your variable? E. Is there a difference based on gender? Perform a p-value test and include the additional steps of a classical hypothesis test at the =.05 level with your data comparing males with females. From information gained in the boxplots decide which gender should be list 1 and list 2 in order to perform a right-tailed test. Does an appropriate confidence interval verify your results? Explain. F. Is your variable (all 50) correlated with the other variable (math or verbal) from your college. For example, if your variable is College 1 Verbal then you would see if College 1 Math is correlated. DO NOT USE SORTED DATA. Remember each subject has a verbal and a math score and you are seeing if there is a linear relationship. 1. Remove all outliers from both lists. Report what you deleted. 2. Create a scatter plot (Use Stat Crunch) 3. Report the correlation coefficient r. 4. Also compare r with the critical value for n = 50 of .279. 5. What is the coefficient of determination? Explain its meaning. 6. What is the linear regression equation of the paired data? Can it be used to predict scores? Explain