A math class consists of 29 students, 17 female and 12 male. Three students are selected at random, one at a time, to participate in a probability experiment (selected in order without replacement).

(a) What is the probability that a male is selected, then two females?

   

(b) What is the probability that a female is selected, then two males?

   

(c) What is the probability that two females are selected, then one male?

   

(d) What is the probability that three males are selected?

   

(e) What is the probability that three females are selected?

   

1. Fifteen students were registered in Section 1 and 15 students were registered in Section 2 of a research course. They took the same midterm exam, and their exam scores were distributed as follows:

Section 1:          89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94

Section 2:           77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98

1. Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Include your SPSS output below. (10 pts)
2. Which section did better overall on the exam? Fully justify your answer using the concepts in W&G Chapter 3. (3 pts)

In recent decades, U.S. students have not done particularly well on standardized tests compared to students in many other countries. What reforms in education have been undertaken to address the perceived quality of the U.S. educational system? Based on what you've learned and read, why do you think test performance isn't better?

Students are potential buyers of editing services for papers they write. Students A-G have Willingness-to-Pay for revisions as follows:

Student WTP($) A 15
B 13
C 11 D9 E7 F6 G4 H2

Suppose that the opportunity cost of editing is a constant $5 (MC=ATC=$5) and that there are many potential suppliers of editing services who are price-takers. What will the equilibrium price and quantity of editing services (how many papers will be edited at what price?). Why? What are consumer, producer and total economic surplus in this equilibrium.

Now suppose that you have been granted a monopoly in providing editing services. Suppose you must set a single price for everyone. .Find your marginal revenue schedule. Then use it to say what quantity of papers you will edit and what price you will charge to maximize profits. Explain. What will consumer, producer and total surplus be now? Compare to the competitive outcome.

Now suppose that you can practice perfect price discrimination. How many papers will you edit and what will your profits be? Explain. What are consumer, producer and total surplus now?

Finally, suppose that the WTP schedule above represents a single student’s WTP for successive papers edited during the semester. (He is willing to pay $14 for the first, $12 for the second, etc.) Your market consists of 100 students just like this one. Design a two-part pricing scheme that maximizes your profits. What fee will you charge and what price per paper edited? Explain.

Sample grade point averages for ten male students and ten female students are listed. Find the coefficient of variation for each of the two data sets. Then compare the results

Males 2.5 3.8 3.6 3.9 2.6 2.6 3.6 3.2 3.9 1.8

Females 2.8 3.5 2.1 3.7 3.5 4.1 2.1 3.9 3.9 2.3

The coefficient of variation for males is ​__%.

The Coefficient of variation for females Is __ %

A.

College Students’ Recent Life Experiences. Researchers administered to 216 undergraduate students (in the same time period) the Inventory of College Students’ Experiences and a measure of daily hassles. The total coefficient alpha was .92 for the Inventory and .96 for the measure of daily hassles. The Inventory correlated with daily hassles at .76 (p <. 001).

B.

Test scores for the Eysenck Personality Inventory and Cattell’s 16 Personality Factor Questionnaire (16PF) were obtained for male army applicants for flyer training. Forms A and B were used for each test and the correlations between forms for the same test ranged from .39 to .85. Some of the men entered flying school several years after taking the tests. The correlations of the subscales on the two tests with training outcome (pass or fail) averaged about .20.

C.

Computer Aptitude and Computer Anxiety. Researchers gave 162 students enrolled in computer courses a test that measured computer anxiety and another that measured computer aptitude. Both were given at the beginning of the course. Student performance in the course was measured by the grades they earned in the course. Computer aptitude was correlated with course grade at .41 (p <. 01) for one course and .13 (p < ns) for the other. Correlations of computer anxiety and course grade were .01 and .16 (p < ns).

Identify the following for each of the studies above:

Predictor(s)

Criterion

Type of validity estimated

Validity Coefficient

Reliability Coefficient

1. A random sample of 2,500 students is taken from the population of all part-time students in the United States, for which the overall proportion of females is 0.6.

There is a 95% chance that the sample proportion (p̂) falls between ______ and _______.

2. The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2009-2010 was $2,450. Assume that the standard deviation in Pell grant awards was $520.

If we randomly sample 40 Pell grant recipients and record the mean Pell grant award for the sample, then repeat the sampling process many, many times, what is the mean and standard deviation of the sample means?

Round your answers to the nearest dollar. Do not include commas in your answer.

Mean:

Standard Deviation:

3. The annual salary of teachers in a certain state X has a mean of $54,000 and standard deviation of σ = $6000.

What is the probability that the mean annual salary of a random sample of 32 teachers from this state is less than $53,000?

Round your answer to four decimal places.

A total of 23 Gossett High School students were admitted to State University. Of those students, 7 were offered athletic scholarships. The school’s guidance counselor looked at each group’s summary statistics of their composite ACT scores, wondering if there was a difference between the groups (those who were not offered scholarships and those who were). The statistics for the 16 students who were not offered scholarships are x̅ = 24.7, s = 2.8 and for the 7 who were, x̅ = 26.5, s = 2.6. Assume that both distributions are approximately normal. Test the counselor’s claim using a 90% Level of Confidence.

We use statcrunch and the p method for homework.

You took independent random samples of 20 students at City College and 25 students at SF State. You asked each student how many sodas they drank over the course of a year. The sample mean at City College was 80 and the sample standard deviation was 10. At State the sample mean was 90 and the sample standard deviation was 15. Use a subscript of c for City College and a subscript of s for State.

1. Calculate a point estimate of the difference between the two population means.

2. Calculate the appropriate number of degrees of freedom to use for your analysis. Hint: Remember that you always round down for degrees of freedom if you get a decimal answer. Note: To calculate this answer you must use the formula which assumes unequal variances.

3. Determine a 95% confidence interval for the difference between the two population means.

4. Give the null and alternative hypotheses for a hypothesis test to test to see if there is a statistically significant difference in the population means between students at the two schools.

5. State α using the confidence level in question 3.

6. Calculate the value of the test statistic.

7. Find a range for the p-value.

8. What is your conclusion in statistical terms?

9. Explain the meaning of this conclusion in business terms.

10. What statistical conclusion would you reach using the confidence interval approach? Explain how you reach this conclusion. Is it the same conclusion you reached using the p-value approach?