You’re running an experiment to determine whether students perform better if they are rewarded with candy or vegetables. You sample 5 students from your class and you first reward the students with vegetables when they get right answers in the class. Then you test them and record their scores. Next, with a different 5 students you reward these students with cookies when they get right answers in the class. Then you test them with another test and record their scores. The following table depicts grades for the two conditions:

The standard deviation for the candy group is 0.25, and the mean is 3.75. The standard deviation for vegetable group is 0.25, and the mean is 2.75.

a. Identify the name of the test you will be employing.

b. Conduct a formal null hypothesis significance test

In a university games tournament, 64 students are about to participate in a chess knockout competition.

The first round consists of 32 games, with two students per game.

The 32 winners of the first round get to play in the second round, which consists of 16 games, and so on, until an overall winner is declared in the sixth round. (In the case of a draw on any game, a coin is tossed to determine the winner.)

(a) In how many different ways can the 64 participating students be paired up on the first round? (Do not consider the order in which students can be paired up.)

(b) Suppose that the 64 participating players are of equal ability, and pairing up is purely random on each round. Find the probability that Eva and Brett (two of the 64 students) will get to play each other at some stage during the knockout competition

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a) A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 40 current students discovering that 15 will return for summer school.At 90% confidence, compute the margin of error for the estimation of this proportion.

b) A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 36 current students discovering that 16 will return for summer school.At 90% confidence, compute the lower bound of the interval estimate for this proportion.

c) A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the university would like a 0.90 probability that the sample proportion is within 0.101 or less of the population proportion.What is the smallest sample size to meet the required precision? (There is no estimation for the sample proportion.) (Enter an integer number.)

Fifteen students from Poppy High School were accepted at Branch University. Of those students, six were offered academic scholarships and nine were not. Mrs. Bergen believes Branch University may be accepting students with lower ACT scores if they have an academic scholarship. The newly accepted student ACT scores are shown here.

Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27

Part A: Do these data provide convincing evidence of a difference in ACT scores between students with and without an academic scholarship? Carry out an appropriate test at the α = 0.02 significance level. (5 points)

Part B: Create and interpret a 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship. (5 points)

Last semester, the students in my Finite Math class had an average quiz score of 83 with a standard deviation of 2. Assume that the scores are approximated by a normal distribution. a) What percent of students scored higher than an 86 on the quiz? b) What percent of students scored less than a 79 on the quiz? c) What percent of students scored between a 79 and an 86? d) What happens when you try to find the percent of students that scored less than a 60?

Problem 3: You play a game where you spin a spinner with the numbers 1 through 10 on it in equal parts. It costs $7 to play. If you spin a two then you win $25. If you spin an odd number then you win $10. You decide to play the game once. What are your expected winings?

Twenty students from Sherman High School were accepted at Wallaby University. Of those students, eight were offered military scholarships and 12 were not. Mr. Dory believes Wallaby University may be accepting students with lower SAT scores if they have a military scholarship. The newly accepted student SAT scores are shown here.

Military scholarship: 850, 925, 980, 1080, 1200, 1220, 1240, 1300
No military scholarship: 820, 850, 980, 1010, 1020, 1080, 1100, 1120, 1120, 1200, 1220, 1330

Part A: Do these data provide convincing evidence of a difference in SAT scores between students with and without a military scholarship? Carry out an appropriate test at the α = 0.05 significance level. (5 points)

Part B: Create and interpret a 95% confidence interval for the difference in SAT scores between students with and without a military scholarship.

A university wants to study the experience of students enrolled in its big classes, defined asclasses with enrollments of 500 or more. There are 20 such classes. From each of these classes,one enrolled student is chosen uniformly at random to take part in the university’s survey. Youcan assume that the selection from each class is performed independently of the selections inthe other classes. In this scenario: (T / F)

1. The method of sampling produces a probability sample of students enrolled in the big classes. (T / F)

2. The method of sampling produces a simple random sample of students enrolled in the big classes. (T / F)

3. Because a student is chosen from each class, all students in the big classes have the same chance of being selected. (T / F)

4. Because a student is chosen from each of 20 big classes, there will be 20 students in the sample. (T / F)

6.73 Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 95, and the standard deviation is about 20. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score is ¯x = 103.3.

1. Assuming that σ = 30 for the population of older students, carry out a test of

   H₀: μ = 95

   H_a: μ > 95

   Report the P-value of your test, and state your conclusion clearly.

2. Your test in part (a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?