statistics problem set

1. Write the formula for the test statistic to use when testing the hypothesis: Ho : p = po vs H1 : p x po at the level of significance of o with n observations and not knowing the population variance, Question 1 (5 pts) ???? Write your answer using notation like this: (a) sqrt (n) for vn (b) (a+b+c) /2 for (atbig) (c) z_ (alpha/2) for subscripts like za and y * 2 for superscripts like y? 2. Boys were given a spelling test. The mean grade of 32 boys was 72 with a sample standard deviation of 8. Test the hypothesis that their average grade is less than 75 at a level of significance of .05. (a) Question 2 (5 pts) a =??? One-sided test or two-sided test ????? n-1=???? (b) Question 3 (5 pts) tal,Is -???? (c) Question 4 (5 pts) T' = 12 7272 - -2.12 732 (d) Question 5 (5 pts) Is T to)=.01 where df=8. to -???? 4. STAT51 students counted the number of e's for an experiment in counting on the first day of class. The average number of e's from the 47 students is 218.957 with a sample standard devia- tion of 71.143.(a) Test the hypothesis that the class average equals the true value of 315 versus the alternative hypothesis that the class average is less than the true value. Use a.05 level of significance. i. a - .05 ii. tacos # 1.67866 iii. Question 9 (5 pts) T - 218 318 987-314 - -9.255129 iv. Question 10 (5 pts) Reject or not reject the null hypothesis ???? Why ???? v. Question 11 (5 pts) Is this a one-sided or two-sided test? ???? Explain ???? (b) Construct a 90% confidence interval about the mean for the number of e's which the STAT51 students counted. i. a - .102 - .05n-1 = 46 ii. to-1,2 - t46,.0 = 1.6759 iii. Question 12 (5 pts) a = 1 - 2 1,= =??!? iv. Question 13 (5 pts) b = ???? v. Question 14 (5 pts) 90% CI is: ????? vi. Question 15 (5 pts) (5 pts) Why is the confidence interval for the STAT51 stu- dents so far away from the true number of e's? ???? Histogram of Samph #13 5. A simulation of the theory of confidence intervals taken from what would have been Computer Assignment #3 if it were assigned was performed by producing 20 sets of 30 randomly generated numbers based on a U(3, 7) probability distribu- tion. The average of 600 random numbers is 4.943. A pic- ture of those 30 random numbers taken from set number 13 is shown here. The sample mean associated with sample # 13 is 5.466667 with sample deviation of 1.431983. (a) Question 16 (5 pts) Why is the histogram not perfectly flat? ???? (b) Let V be a random variable which is distributed as stated above. Compute the expected value and variance of V. Note: E[V] - 9: and var(V) _ (6 )(b at?) i. Question 17 (5 pts) E[V] - ???? ii. Question 18 (5 pts) var(V) - ???? 2(c) Define V= 20 i. Question 19 (5 pts) Compute E[V] - ???? ii. Question 20 (5 pts) Compute var(V) = ???? 6. BONUS Question 21 (5 pts) Write the missing Greek name above each Greek letter. ?7?? kappa omicron pi omicron ???? sigma A P O 5 7. BONUS Question 22 (5 pts) This hill the name of which is written in Greek and upon which many famous buildings were constructed is located in Athens. What is its name in English