A Community Center was interested in the effect of their program on summer loss. Summer loss is the decrease in academic knowledge from the summer to the Fall of the new year. To test their program, they drew a random sample of 20 students from the program. The students were assessed before and after the 6 week program on a 36 item assessment. Difference scores were calculated for the 20 students and are summarized below. (These scores were calculated by subtracting the pretest from the post test score.) Difference Scores on Assessment Pre-Post Program (N=20) 2 -6 0 0 6 2 6 6 3 6 6 3 3 3 3 0 2 1 3 1

At .01 significance level, do the results support the effectiveness of the program slowing summer loss?

Create a 90 % confidence interval. How does the confidence interval support your decision?

The national average of college students on a test of sports trivia is 50 with a standard deviation of 5. A sportscaster is interested in whether BC students know less about sports than the national average. The sportscaster tests a random sample of 25 BC students and obtains a mean of 48 Use an alpha level of 0.05.

1. State the z score(s) that form the boundaries of the critical region. Use an alpha level of 0.05.

2. Calculate the standard error

3. Calculate the z score

4. What decision would you make? Fail to reject the null hypothesis or Reject the null hypothesis

5. What can the researcher conclude? Let’s say in the above example that the BC average on the sports trivia test was 52 resulting in a z score of +2.0. What decision would the researcher make? Fail to reject the null hypothesis? or reject the null hypothesis?

6. Why did you make that decision in Question 5?

6.27  Average hours per week listening to the radio. The Student Monitor surveys 1200 undergraduates from four-year colleges and universities throughout the United States semiannually to understand trends among college students.¹¹ Recently, the Student Monitor reported that the average amount of time listening to the radio per week was 11.5 hours. Of the 1200 students surveyed, 83% said that they listened to the radio, so this collection of listening times has around 204 (17% × 1200) zeros. Assume that the standard deviation is 8.3 hours.

1. (a) Give a 95% confidence interval for the mean time spent per week listening to the radio.

2. (b) Is it true that 95% of the 1200 students reported weekly times that lie in the interval you found in part (a)? Explain your answer.

3. (c) It appears that the population distribution has many zeros and is skewed to the right. Explain why the confidence interval based on the Normal distribution should nevertheless be a good approximation.

Does daily exposure to bright light make subjects more alert? A study was conducted in which the daily habits of 60 college students were documented, focusing on how much time they spent in brightly lit rooms or outside on sunny days. After a week, the subjects were given a computer-based alertness test on which they received a score on a 0 to 100 point scale. Their scores were compared with how much time they spent in brightly lit places that week.

Select one or more:

A. The explanatory variable is how much time the students spent in brightly lit places.

B. This study is best described as an observational study.

C. The explanatory variable is the score on the computer-based test.

D. This study is best described as an experiment study.

E. The response variable is the score on the computer-based test.

F. The response variable is how much time the students spent in brightly lit places.

At one college, the proportion of students that needed to go into debt to buy their supplies each term (books, tech, etc.) was once known to be 74%. An SRS of 60 students was then surveyed in a later term, in order to see if this previous proportion would still be supported by the new sample evidence.

Out of these 60 sampled students, 52 needed to go into debt to buy their supplies that term. Using a normal distribution of approximation (according to the CLT): We will conduct a two-sided significance test at a 3% significance level, to see if our sample has produced statistically significant evidence.

1. State the hypotheses (both the null and alternative) for this two-sided significance test.

2. Using N(μ, σ) normal distribution notation: Identify the very specific normal distribution (by stating the exact numerical values for μ and σ within this notation) that should be used to perform this test.

3. Find the percent P-value from this test.

Stage 1 ABC at a College: Assigning Costs to Activities
An accounting professor at Middleton University devotes 60 percent of her time to teaching, 30 percent of her time to research and writing, and 10 percent of her time to service activities such as committee work and student advising. The professor teaches two semesters per year. During each semester, she teaches one section of an introductory financial accounting course (with a maximum enrollment of 40 students) and one section of a graduate financial accounting course (with a maximum enrollment of 25 students). Including course preparation, classroom instruction, and appointments with students, each course requires an equal amount of time. The accounting professor is paid $84,000 per year.

Determine the activity cost of instruction per student in both the introductory and the graduate financial accounting courses.

Round answers to two decimal places.

A 7th grade science teacher was interested in knowing if his after-school tutoring sessions would boost grades for the students in his classes. The sample consisted of all the children in his 4th and 5th hour classes. The teacher gave a pre-test to each class. Then he held twice weekly sessions for 1 hour after school for four weeks. Students required permission from their parents/guardians in order to attend. Approximately 3/4 of the students for both hours attended. At the end of the 4th week, the teacher gave a post-test and measured the gains/losses in scores. He noted a significant increase in scores and attributed those gains to his tutoring sessions.

1. Identify at least two potential threats to the validity of his study and therefore to the results.

2. Discuss the threats - how might they affect the study results?

3. Propose a method for each threat to reduce/eradicate it.

2. To study the effect of caffeine on cognitive ability, a cognitive ability test was administered to 8 students under two conditions on different days: Condition A) Without caffeine, and Condition B) after the students enjoyed a pumpkin spice latte. The students were randomized to determine if they did Condition A first or Condition B first (on separate days). The following are the results from the test:

• (a) Estimate a 90% confidence interval for the change in test score between Condition A and condition B.
• (b) Determine if there is evidence that caffeine improved performance on the cognitive ability tests at a fixed Type I error rate of 0.05.
• (c) What is the level of significance of the test that you conducted in part (b).

a. all Hypothesis Tests must include all four steps, clearly labeled;

b. all Confidence Intervals must include all output as well as the CI itself

c. include which calculator function you used for each problem.

2. An experiment was done to see whether open-book tests make a difference. A calculus class of 48 students agreed to be randomly assigned by the draw of cards to take a quiz either by open-notes or closed-notes. The quiz consisted of 30 integration problems of varying difficulty. Students were to do as many as possible in 30 minutes. The 24 students taking the exam closed-notes got an average of 15 problems correct with a standard deviation of 2.5. The open-notes crowd got an average of 12.5 correct with a standard deviation of 3.5. Assume that the populations are approximately normal. At the 5% significance level, does this data suggest that differences exist in the mean scores between the two methods?

Use the information to answer Q7-10 Clemson found that 6% students said that they were strongly opposed to increases in college tuition. Suppose we have a random sample of 200 students. Let ?̂be the sample proportion.

7. The mean of ?̂is ____.

8. The standard deviation (sometimes called standard error) of ?̂is ____. (4 decimal places)

9. Which of the following can best describe/explain the shape of ?̂?

A. We can’t determine the shape of ?̂.

B. ?̂follows normal distribution because: 1. The sample is random. 2. ? is large enough

C. ?̂follows normal distribution because: 1. The sample is random. 2. ? = 200 ≥ 30.

D. ?̂follows normal distribution because: 1. The sample is random. 2. ?? = 0.06(200) = 12 ≥ 5 and ?(1 − ?) = 0.94(200) = 188 ≥ 5.

10. What is the probability that more than 13 students out of this sample of size 200 are strongly opposed to increases in college tuition. (4 decimal places)