What is the statistic used developing the decision rule for each of the following problems

01. What is the statistic used developing the decision rule for each of the following problems.  If the statistic used is the student t distribution you must indicate the sign or signs of the critical t value. For example, for 6f the statistic is the student t distribution with a positive sign.  All that is needed for the answer is “statistic is the student t distribution (can just write t) with a positive sign”.  Anything else will lead to that section of the problem being graded as incorrect.  To repeat, no calculations are necessary.  All that is needed is just “statistic is a t, r, 2 or F and the sign(s) if it is a t”.

a.    SAT scores predict college grade point averages. Sample data: n = 25. Use the 99% confidence level.
b.    Dr. Pepper Company claims that Dr. Pepper, Pepsi and Coca-cola have the SAME carbonation level.  Sample data: n = 20. Use the 95% confidence level.

c.    The chairperson of NOW claims that being left-handed is INDEPENDENT of gender. Use the level of significance = 0.05.

d.    When dropped from a standardized height, yellow baseballs have bounce heights DIFFERENT from the mean bounce heights of 92.84 inches obtain in previous studies with white baseballs.  Sample data for the yellow baseballs: n = 40, mean = 92.67 inches, s = 1.79 inches. Use level of significance = 0.05. Does it appear that the yellow and white baseballs are different?

e.    The mean life span of desktop PCs is LESS than 7 years.  Sample data: n = 21, mean = 6.8 years, s = 2.4 years.  Level of significance = 0.05.
f.    The mean IQ score of statistics professors is GREATER than 120. Sample data: n = 12, mean = 132 and s = 12. Us 0.05 as the level of significance.

  

02.    Write the null hypothesis and the alternate hypothesis IN WORDS for each for each of the claims listed in Problem #01 above.  SHORTHAND NOMENCLATURE WILL BE GRADED AS INCORRECT.  Therefore the use of any signs, such as =, will be counted as incorrect.
                   
EXTRA CREDIT WORTH UP TO 12 POINTS:  What are the actual critical values for Problem #1?  For example for 1f, the answer is t = + 1.796.  Each part of the problem is worth 2 points.


03.    The University of HARDTOGETINTO requires all applicants to submit their scores on the Scholarship Aptitude Scoring for Soreheads (SASS) examination.  SASS is a standardized examination with a mean set at 50 and a standard deviation at 15.  In order to get admitted an applicant must have a standardized SASS score of at least 76 and a high school grade point average of at least 3.25

Robert has applied for admission to the University.  Robert has a high school grade point average of 3.56 and answered 155 questions correctly on the SASS examination.  On this particular examination the national raw scores mean for correct answers was 125 and the standard deviation was 20.

As an admission officer you must determine Robert’s admission status.  Therefore, you need to know his standardized SASS score.  What is Robert’s standardized SASS score?  Did you grant Robert admission to the University of HARDTOGETINTO?


04.    Use the data in Problem #03 to answer this Problem:
a.    Assuming the SASS scores are symmetrically distributed with the mean and standard deviation listed in Problem #08 and these reflect the distribution of SASS scores for applicants with at least a high school GPA of 3.25, what percent of these applicants are admitted to the university?

b.    Assuming the SASS scores are symmetrically distributed with the mean and standard deviation listed in Problem #08 and these reflect the distribution of SASS scores for applicants with less than a high school GPA of 3.25, what percent of these applicants are admitted to the university?

c.    What percent of the applicants with at least a 3.50 high school GRA are admitted to the University?