The registrar of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: Of the first-year students in a particular year, 80% successfully complete their course of studies and move on to the second year, whereas 20% drop out of the program; of the second-year students in a particular year, 92% go on to the third year, whereas 8% drop out of the program; of the third-year students in a particular year, 98% go on to graduate at the end of the year, whereas 2% drop out of the program.

(a) Construct the transition matrix associated with the Markov process. (Label your matrix using this order: Drop out, Graduate, First-Year, Second-Year, Third-Year)

(b) Find the steady-state matrix. (Round your answers to four decimal places.)

(c) Determine the probability that a beginning law student enrolled in the program will go on to graduate. (Round your answer to four decimal places.)

You are asked to investigate the impact of diabetes on elementary school students’ academic performance. You decide to test whether the mean standardized test performance of students with diabetes is worse than the test performance of the school as a whole. The school has 235 students and the average test score for the school is set at 100 and has a standard deviation of 25. You are given data from 10 diabetic students who have an average score of 80. Please use a significance of 0.01.

a. Identify the assumed sample distribution, the formula for the test statistic, the significance level, the test distribution, and the null & alternative hypotheses

b. Calculate and report the test statistic, the input values for the test statistic, and the p value that results from the test. Also calculate the statistical power.

c. Decide whether you will reject or fail to reject the null hypothesis. Interpret that decision in the context of the problem. Evaluate the statistical power.

A dietetics student wanted to look at the relationship between calcium intake and knowledge about calcium in sports science students.

Research question: Is there a relationship between calcium intake and knowledge about calcium in sports science students?

Hypotheses: The 'null hypothesis' might be: H0: There is no correlation between calcium intake and knowledge about calcium in sports science students (equivalent to saying r = 0)

And an 'alternative hypothesis' might be: H1: There is a correlation between calcium intake and knowledge about calcium in sports science students (equivalent to saying r ≠ 0)

A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 214 students using Method 1 produces a testing average of 53.9. A sample of 193 students using Method 2 produces a testing average of 88.9. Assume that the population standard deviation for Method 1 is 17.61, while the population standard deviation for Method 2 is 11.73. Determine the 99% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2.

Step 1 of 3:

Find the point estimate for the true difference between the population means.

Step 2 of 3:

Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

Step 3 of 3:

Construct the 99%99% confidence interval. Round your answers to one decimal place.

Thousands of college students are attending a political conference and are about to enjoya dinnerbanquet. The probability a randomly selected student is a Democrat is .70. The probability a randomly selected student is a Republican is .30.Before the banquet, students were asked what they wanted for dinner. Their options were a vegetarian dish, beef, or chicken.Among the Democrat students, the proportion who requested the vegetarian dish was .20, the proportion who requested beef was .30, and the proportion who requested chicken was .50.Among the Republican students, the proportion who requested the vegetarian dish was .10, the proportion who requested beef was .50, and the proportion who requested chicken was .40.Draw a tree diagram and use it to answer these questions:3aIf a student is selected at random, what is the probability they are both a Democrat and requested chicken for dinner?3bIf a student is selected at random, what is the probability they requested the vegetarian dish for dinner?3cGiven that a randomly selected student requested beef for dinner, what is the probability they are a Republican?

1. Use the following information for the next three problems.  Suppose that  = 30% of the students at a large university must take a statistics course.  Suppose that a random sample of 50 students is selected.  Let  = the percent of students in the sample who must take statistics.

   Different samples will produce different values of .  In order for the values of  to vary according to a normal model, we need to check two conditions.  Which two of the following need to be checked?

   	a.	The sample size  is large ().
   	b.	The sample observations are independent of each other.
   	c.	and
   	d.	The population distribution is normal in shape.

QUESTION 4

1. 95% of all samples will produce a  between __________ and __________.

   	a.	0.235 and 0.365
   	b.	0.280 and 0.320
   	c.	0.105 and 0.495
   	d.	0.170 and 0.430

QUESTION 5

1. What is the chance that more than 38% of the students in a sample must take statistics (i.e. what is the chance that  > 0.38)?

   	a.	0.6480
   	b.	0.8907
   	c.	0.1093
   	d.	1.23

Quiz vs Lecture Pulse Rates

Do you think your pulse rate is higher when you are taking a quiz than when you are sitting in a lecture? The data in Table 1 show pulse rates collected from 10 students in a class lecture and then from the same students during a quiz. The data are stored in QuizPulse10.

Table 1 Quiz and lecture pulse rates for 10 students

Construct a 99% confidence interval for the difference in mean pulse rate between students taking a quiz and sitting in a class lecture.

Heights for preschool aged students are approximately normally distributed with a mean of 40 inches and a standard deviation of 2.3. Lilly is a preschool student who is 43.5 inches tall.

A. Using the empirical rule, what percent of preschool aged students are between 37.7 inches tall and 46.9 inches tall? Do not round your answer. Make sure your answer includes a percent sign. 93.57%

B. Using the standard normal distribution table, what proportion of preschool aged students are shorter than Lilly? Do not round your answer from the table. .68

C. Using the standard normal distribution table, what proportion of preschool aged students are taller than Lilly? Do not round your answer from the table.

D. Sophie is also a preschool aged student. Her doctor tells her parents that Sophie's height is in the 23rd percentile. What is Sophie's height? Do not round your answer.

Use the following information for the next three problems.  Suppose that  = 30% of the students at a large university must take a statistics course.  Suppose that a random sample of 50 students is selected.  Let  = the percent of students in the sample who must take statistics.

Different samples will produce different values of .  In order for the values of  to vary according to a normal model, we need to check two conditions.  Which two of the following need to be checked?

2. 95% of all samples will produce a  between __________ and __________.

3. What is the chance that more than 38% of the students in a sample must take statistics (i.e. what is the chance that  > 0.38)?