Write the EBNF for mini Java language based of the following information:

Data Types

• Integer
  • Int
  • Long
• Double
• Boolean
• Char
• References

Complex Data Structures

• Arrays
  • int v[30];
• Classes
  • member variables
    • class Name {
    • int a;
    • char b;
    • char name[25];
    • }

Methods

• Return data type
  • Primitive data type
  • Void
• Method Name
• Parameter list
  • Could be empty
• Statement Block
  • {
  • Variable declarations
  • Executable Statements
  • }

Program

• Variable Declarations
• Class Definitions
• Methods
• Only one method named "main" but must have one method named main

Statements

• Expression Statements
  • Assignment operation allowed in expressions
  • Add, Sub, Mult, Divd, 6 comparisons, Logical operations (and, or, not), Assignment
• If statements
  • else is allowed but optional
• While statements
• Print
  • eol value to go to new line
  • allow multiple print items
• Return statement - returns the value of an expression

Statement Blocks

• Enclosed in braces
• Separate statements using semicolons

The College of UCLA investigated differences in traditional and nontraditional students, where nontraditional students are defined as 25 years or older and working. Based on the study results, it was assumed that the population mean and standard deviation for the GPA of nontraditional students is µ = 2.75 and ? = 0.56.

a. Suppose a random sample of 49 nontraditional students is selected and each student's GPA is calculated. The probability that the random sample of 49 nontraditional students have a mean GPA less than 2.57 is . Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

b. Fifty-four percent of the samples of n = 49 students drawn from this population will have a sample mean GPA of at least . Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 7 students, taught in traditional lab sessions, had a mean test score of 79.6 with a standard deviation of 3.3. A random sample of 15 students, taught using interactive simulation software, had a mean test score of 84.9 with a standard deviation of 5. Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ1 be the mean test score for the students taught in traditional lab sessions and μ2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 4: State the null and alternative hypotheses for the test.

Suppose you are a researcher studying the study habits of college students. The parameter you wish to measure is the number of minutes students study each week. From previous research you know that this parameter is distributed Normally and has a standard deviation of 50 minutes. (Please only answer one part at a time to give other students a chance to answer as well! Start with the first one!)

1. If you wish to construct a 90% confidence interval that has a margin of error of 5 minutes, how many students do you need in your sample?

2. Suppose you wish to construct a 90% confidence interval that has a margin of error of only 2 minutes. How will this affect the number of students you need in your sample? How many students will you need?

3. Repeat the calculation in Part (1) above for an 80% confidence interval.

4. Repeat the calculation in Part (2) above for an 80% confidence interval.

(a) Two website designs are being compared. 54 students have agreed to be subjects for the study, and they are randomly assigned to visit one or the other of the websites for as long as they like (i.e., half of this number are assigned to visit each of the websites) . For each student the study directors record whether or not the visit lasts for more than a minute. For the first design, 13 students visited for more than a minute; for the second, 6 visited for more than a minute. Find the large-sample 95% confidence interval for the difference in proportions (±0.001). The interval is from to (b) Samples of first-year students and fourth-year students were asked if they were in favor of a new proposed core curriculum. Among the first-year students, 85 said "Yes" and 272 said "No." For the fourth-year students, 115 said "Yes" and 104 said "No.". Find the large-sample 95% confidence interval for the difference in proportions (±0.001). The interval is from to

Consider the following research hypothesis and the p-value obtained via a statistical test. Would this testing have involved one-sample or two-sample hypothesis testing? Does the scenario involved paired or independent samples? Assuming the appropriate testing was used, what would be an appropriate conclusion to draw given the reported results and p-value?

Explain the reasoning for your answers.

The hypothesis is that students who are familiar with the Theory of Algorithms learn the programming language C++ faster than students who are not familiar with this theory. We have gathered data from 30 students who are familiar with the Theory of Algorithms (Group 1) and 30 students who are not familiar with the Theory of Algorithms (Group 2). Experiments showed students from Group 1 took a mean of 32.5 hours to complete the training course of C++, while students Group 2 the mean was 42.1 hours. The p-value was 0.14.

Students’ interactions with universities create large amounts of data. The data is generated in several main areas. Firstly, students provide data as part of their application and enrolment process, including entrance and demographic data. Secondly, students’ interactions with the school website generate data, and thirdly, students’ performance data is collected in the student information system. Universities can use this data in many ways by combining and aggregating the data from these difference sources and analysing it for patterns, trends and causal relationships between certain behaviours and outcomes.
Note: (For this, you will have to google "Learning Analytics" if you don't specifically know what it is.)

Q1. Discuss the benefits that could arise to students from Learning Analytics.

Q2. Discuss the benefits that could arise to a university from Learning Analytics.

Q3. Describe some possible negative outcomes for students from Learning Analytics.

Q4. Do you think the collection and analysis of student-relating data is ethical?

Consider the following research hypothesis and the p-value obtained via a statistical test. Would this testing have involved one-sample or two-sample hypothesis testing? Does the scenario involved paired or independent samples? Assuming the appropriate testing was used, what would be an appropriate conclusion to draw given the reported results and p-value? Explain the reasoning for your answers.

The hypothesis is that students who are familiar with the Theory of Algorithms learn the programming language C++ faster than students who are not familiar with this theory. We have gathered data from 30 students who are familiar with the Theory of Algorithms (Group 1) and 30 students who are not familiar with the Theory of Algorithms (Group 2). Experiments showed students from Group 1 took a mean of 32.5 hours to complete the training course of C++, while students Group 2 the mean was 42.1 hours. The p-value was 0.14.

Northwood and Eastwood are rival schools that wish to compare how their students did in a math competition. 72 randomly chosen Northwood students participated and received a mean score of 28 with a standard deviation of 8, 98 randomly chosen Eastwood students participated and received a mean score of 25 with a standard deviation of 10.

(a) The Eastwood math teacher wants to show through statistics that her students receive a higher mean score in the contest. State her hypotheses. (2 points)

(b) Compute the test statistic and p-value for this test. (6 points)

(c) Reach your conclusion at the 0.05 significance level. Be sure to interpret in the context of the problem. (2 points)

(d) In a separate test, the Eastwood teacher finds evidence that Eastwood students performed better than Southwood students. Would this prove that the Eastwood teacher was more effective than the Southwood teacher? Explain briefly. (3 points)

Consider the following research hypothesis and the p-value obtained via a statistical test. Would this testing have involved one-sample or two-sample hypothesis testing? Does the scenario involved paired or independent samples?
Assuming the appropriate testing was used, what would be an appropriate conclusion to draw given the reported results and p-value?
Explain the reasoning for your answers.
The hypothesis is that students who are familiar with the Theory of Algorithms learn the programming language C++ faster than students who are not familiar with this theory. We have gathered data from 30 students who are familiar with the Theory of Algorithms (Group 1) and 30 students who are not familiar with the Theory of Algorithms (Group 2). Experiments showed students from Group 1 took a mean of 32.5 hours to complete the training course of C++, while students Group 2 the mean was 42.1 hours. The p-value was 0.14.