Research question: In the population of all Penn State students, are more than 80% enrolled full-time?

In this question set you will be using StatKey to conduct randomization tests for a single proportion. These data are not built in to StatKey, so you will need to “Edit data” to enter in the sample counts. Please show screenshots and work.

B. Using the five steps from the online notes, conduct a randomization test given that 350 students in a sample of 400 are full-time students. Be sure to include your relevant StatKey output. [30 points]

Step 1: Determine what type of test you need to conduct and write the hypotheses.

Step 2: Construct a randomization distribution under the assumption that the null hypothesis is true. Take at least 5000 resamples.

Step 3: Use the randomization distribution to find the p-value.

Step 4: Decide if you should reject or fail to reject the null hypothesis.

Step 5: State a real-world conclusion in relation to the original research question.

Question 2. Consider the market for burritos in Vancouver, blessed with thousands of students and dozens of small burritos stands. The demand and supply schedules are shown in the table.

1. Graph the demand and supply curves. What is the free -market equilibrium in this market?

Answer:

2. What is the total economic surplus in this market in the free-market equilibrium? What area in your diagram represents this economic surplus?

Answer:

3. Suppose the local government, out of concern for the students' welfare, enforces a price ceiling on burritos at the price of $1.50. Show in your diagram the effect on price and quantity exchanged.

Answer:

4. Are students better off as a result of this policy? Explain.

Answer:

5. What happens to overall economic surplus in this marker as a result of the price ceiling? Show this in the diagram.

Answer:

15 highly anxious students were randomly assigned so that 5 received behavioral therapy, 5 received cognitive therapy, and 5 received psychoanalytic therapy. Later all 15 students were tested for anxiety (on a scale where the higher the score the greater the anxiety). The results of these measures appears below. On the basis of these data determine whether the therapies differ in their effectiveness.

          Anxiety Scores for Students Receiving Various Types of Therapy

                       Behavioral     Cognitive       Psychoanalytic

                                5                    5                      8

                                4                    5                      7

                                8                    7                      8

                                7                    7                      6

                                6                    6                      6

a) what is the inferential statistic? (choose one)

•Two-independent-samples t test

•Related-samples t test

•One-way between-subjects ANOVA

•One-way repeated-measures (within-subjects) ANOVA

•Two-way between-subjects ANOVA

•Regression/correlation

•Chi-square test for independence

b) what are the critical value(s)?

c) reject or accept null hypothesis?(yes or no)

An attorney in the Washington Metropolitan area has been in the law profession for several years. Over the years it is known that she has won 60% of all her cases representing her clients. She currently has 15 cases pending. Answer the following questions. Show what you put into the calculator and possible calculations for each part, not just the answers. Think binomial. Use the TI 83 showing all your work.

a. Probability that she will win 10 cases?

b. What is the probability that she will win less than 4 cases?

c. What is the probability that she will win at least 9 cases?

d. What is the probability that she will win more than 8 cases?

e. What is the probability that she will win at most 12 cases?

There are 23 students in a Statistics class. If the mean age of 22 of these students in the class is 22.5 years, find the age of the 23^rd student if the mean age of all the 23 students in the class is 23 years?

A school principal is interested in assessing the performance of her students on the Totally Oppressive Standardized test (TOST). She selects a simple random sample of 16 of her students and finds the following set of test scores:

Assume that the sample is drawn from a population with a standard deviation σ = 7.20.

a. (1 point) What is the mean test score for the sample of students?

13

b. (4 points) Calculate and write a sentence to interpret the 95% confidence interval for the mean test score.

c. (3 points) Calculate and write a sentence to interpret the 99% confidence interval for the mean test score.

13 - 2.58 * (1.8) 13 + 2.58 * (1.8)= 8.3,17.6????

d. (4 points) Explain why the margin of error for the 95% confidence interval in question (b) is smaller than the margin of error for the 99% confidence interval in question (c).

reconsider dr Sameers research question about how much time cal poly students spend watching tv, and recall that for random sample of 100 cal poly students number of hours per day spemt watching tv the mean and SD tunred out to be 3.01 hours and 1.97 hours respectively. a. in the context of thios study, is the theory based approach (one sample t-test) valid to find a p value to investigate whether the data provide evidence that the average number of hours per day cal ply students spend watching TV is different from 2.75 hours? explain b) regardless of your answer in (a) use the theroy based inference aplet to conduct a one sample t test to find and report a standarnized statistic and a p value for dr sameers hypothesis c) state your conclusion from this study based on the p value reported in b being sure to rpovide justification for your conclusion

1) A single card is drawn from a standard 52 card deck. Calculate the probability that a black card or an ace is drawn. (show answer as a reduced fraction #/#)

2)A professor knows from past experience that in a class of 36 students the time for students to complete an exam has an N(50,10) distribution. Suppose that he wants to allow sufficient time so that 98% of the students will complete the exam in the allotted time. How much time should he allow for the exam? (Round to the whole number)

3)

Suppose we are testing the null hypotheses H₀: μ=118 against H_a: μ≠118. Suppose our population is normal with a standard deviation of 12. A random sample of 50 observations are drawn from the population, and we find the sample mean of these observations is 120.

a. Find the P-value is (Round to two decimals throughout and show answer as a percent with two decimals)

b.If α= .10, should we accept H₀ or H_a?  (Show answer as Ho or Ha)

1. the IV(s) and its levels and the DV or the classification variable and its categories and the DV (if chi-square analysis) or the X/Y variables (if correlation or regression)
2. the nature (continuous or discrete) of the DV or the X/Y variables
3. the appropriate statistical analysis

1. Researchers evaluated whether the teen pregnancy rate at a local high school with abstinence-only sex education differed from the average teen pregnancy rate statewide. At the time of the study, the statewide rate (regardless of type of sex-education received) was 12%. A random sample of 200 female students was selected from the local school: thirty-seven of the students were either currently pregnant or had been pregnant previously, whereas 163 students were not/had never been pregnant.

2. White (2001) was interested in the effect of two different types of exercise programs for improving time to run a marathon. He was one of the first researchers to evaluate how each type of exercise program affected the running times for participants of both normal and obese body types.

Analyze if the statements that are presented below are True or False. You MUST justify your answer to get credit. Answers without justification (even if they are correct) will be given zero marks.

1. (a) In any Pareto-optimal allocation of a two-good economy, each consumer has to consume a positive amount of both goods.

2. (b) A monopolist never produces on the elastic segment of its average revenue curve.

3. (c) If a firm’s production exhibits increasing returns to scale, then the firm’s marginal costs are decreasing and below its average costs.

4. (d) Maroon Theater practices third-degree price discrimination and sells tickets to three groups of customers: students, regular customers and senior citizens. The inverse demand of the three groups is linear. Furthermore, the students’ and senior citizens’ elasticities of demand for tickets are −4 and −3, respectively. Because the price charged to regular customers is greater than the price charged to senior citizens, we know with certainty that the ticket price for students will be lower than the ticket price for regular customers.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ? of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.410.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510 .

In answering the questions, use ?‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 505 and 515? (Enter your answer rounded to four decimal places.)

Probability - ?

(b) You sample 2525 students. What is the standard deviation of the sampling distribution of their average score ?¯  ? (Enter your answer rounded to two decimal places.)

Standard Deviation - ?

(c) What is the probability that the mean score of your sample is between 505505 and 515515 ? (Enter your answer rounded to four decimal places.)

Probability - ?