Assume that the mean SAT score of students admitted to Northeastern Illinois University is 1090. The members of the Psychology Department believe that students who decide to major in Psychology have higherSAT scores than the general population of students at the university. A sample of N= 10 newly declared Psychology majors consent to have their entrance records reviewed.

Their scores are as follows: 1276, 1248, 1066, 1106, 1138, 1215, 1168, 1185, 933, and 1425.Can the department conclude that Psychology majors have higher SAT scores than the university as a whole?

(a)Set up your hypotheses using the correct notation (1mark)

(b)Compute tobt(1.5marks)

(c)What is the statistical decision? JUSTIFY YOUR ANSWER (1mark)

(d)What is the conclusion? (1mark)

(e)Compute the 95% Confidence Interval for μ (1 mark)

1. In a recent campus survey, 75 Indiana students were asked if they felt that their education at Cleary was preparing them for their future careers and 83% of students responded “Extremely well prepared.” Construct a 95% confidence interval (use z= 1.96) for the true proportion of Cleary students who feel the same way. Round standard error to 4 decimal places.

2.   Is there anything you could do to get a narrower range of values in the previous problem?

3. Is the sample size of 75 from the previous problem enough to get a 3% margin of error and 95% confidence? (To get full credit find the minimum sample size and then compare to 600 to see if large enough). Again use z=1.96. Also use a p-hat value of 0.83.

The time required for a student to complete an Economics 110 exam is normally distributed with a mean of 54 minutes and a standard deviation of 16 minutes.

5. ______ What percentage of students will complete the exam in less than 75 minutes (before end of class period)? (A) .4049 (B) .9951 (C) .8051 (D) .9049

6. ______ At what point in time (i.e., how long after the exam starts) will one-third of all students have finished taking the exam? (A) 25 minutes (B) 60.9 minutes (C) 47.1 minutes (D) 38.5 minutes

7. ______ In a class of 50 students taking an Economics 110 exam, what is the probability that the average time required to take the exam will be more than 60 minutes? (A) .4960 (B) .0040 (C) .1480 (D) .3520

1a) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A student is randomly selected from the SAT population. What's the probability of that student's score being between 350 and 600?

1b) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A college decides to admit students with SAT scores greater than or equal to 450. Assuming the applicant population contains 1500 students, how many would be admitted?

1c) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A college decides to admit only the top 10% of SAT students. What would its cutoff SAT score be?

Suppose that the national average for the math portion of the College Board's SAT is 513. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 588?

___ %

(b) What percentage of students have an SAT math score greater than 663?

___ %

(c) What percentage of students have an SAT math score between 438 and 513?

___ %

(d) What is the z-score for a student with an SAT math score of 620?

____

(e) What is the z-score for a student with an SAT math score of 405?

____

Suppose that the national average for the math portion of the College Board's SAT is 518. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

Suppose that the national average for the math portion of the College Board's SAT is 518. The College Board periodically rescales the test scores such that the standard deviation is approximately 50. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places. (a) What percentage of students have an SAT math score greater than 568? % (b) What percentage of students have an SAT math score greater than 618? % (c) What percentage of students have an SAT math score between 468 and 518? % (d) What is the z-score for student with an SAT math score of 620? (e) What is the z-score for a student with an SAT math score of 405?

A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 36% of those who come to class on a regular basis receive A's. Only 4% who do not attend regularly get A's. Overall, 60% of students attend regularly. Based on this class profile, suppose we are randomly selecting a single student from this class, and answer the questions below.

Hint #1: pretend that there are 1000 students in the class and use the values given in the problem to construct the appropriate contingency table. Round cell frequencies to the nearest integer

C) P(receives A's) =

D) P(attends regularly | receives A's)

E) P(does not attend regularly | does not receive A's) =

Please create a c++ program that will ask a high school group that is made of 5 to 17 students to sell candies for a fund raiser. There are small boxes that sell for $7 and large ones that sell for $13. The cost for each box is $4 (small box) and $6 (large box). Please ask the instructor how many students ended up participating in the sales drive (must be between 5 and 17). The instructor must input each student’s First name that sold items and enter the number of each box sold each (small or large). Calculate the total profit for each student and at the end of the program, print how many students participated and the total boxes sold for each (small and large) and finally generate how much profit the group made. (15 points)