Question2

Thedatainthetablearesimulatedexamscores.Supposetheexamwasgiveninthesemesterafterthecoursecontentwasrevised,andthepreviousmedianexamscorewas70.

Simulated Answer scores

7974888080666586848078727174869677817680

7675788787748584767776748574767776748176

(a)We would like to know if the median exam score has increased. Answer the question by using the Binomial Test.

(b) Make a 95% confidence interval for the median.

(c) Make a 95% confidence interval for the 75^th percentile.

(d) Make a 95% confidence interval for F(80), the probability that a score is less than or equal to 80.

STAT 445545 Nonparametric Statistics Instructions for All Assignments I Show all your work to get full points. Eur answer only shows R outEit, without supplementary formulas and necessary statistical analysis, you will not get full credit. It is OK to use R to calculate test statistics and pvalues. Supplement results from R with equations to calculate the test statistic and p-value. You do not need to do everything by hand. Your answers must be as complete and clear as possible. Use signicance level o.=0.05 for all tests. Your answers must include the following items: 0 Assumptions I The assumptions for using the Nonparametric test. I Verify each assumption when possible. 0 Sample statistic I o Hypothesis Testing I Null hypothesis and alternative hypothesis. I The formula for calculating the test statistic and the observed test statistic. I The formula for calculating the exact p-value and the pvalue. [t'not possible to get an exact p-value, explain why it is not possible and calculate the p-value using an alternative method. I Your decision about the null hypothesis. I State your conclusion and interpret the conclusion in plain language based on the question 0 Condence Intervals I Give the formula or describe the process used to derive the interval. I Interpret each interval