A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is ready for​ college-level mathematics. To achieve this​ goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 200 students who completed this core set of courses results in a mean math score of 24.3 on the college entrance exam with a standard deviation of 3.6.

Do these results suggest that students who complete the core curriculum are ready for​ college-level mathematics? That​ is, are they scoring above 24 on the math portion of the​ exam? Complete parts​ a) through​ d) below.

a) State the appropriate null and alternative hypotheses. Fill in the correct answers below.

The appropriate null and alternative hypotheses are H0​:_____ ______ _____ H1​: ______ _______ _____

​b) Verify that the requirements to perform the test using the​ t-distribution are satisfied. Check all that apply.

A. The students were randomly sampled.

B. The sample size is larger than 30.

C. The​ students' test scores were independent of one another.

D. None of the requirements are satisfied.

​c) Use the​ P-value approach at the a=0.05 level of significance to test the hypotheses in part​ (a).

Identify the test statistic.

Identify the​ P-value.

​P-value=________ ​(Round to three decimal places as​ needed.)

​d) Write a conclusion based on the results. Choose the correct answer below.

_________the null hypothesis and claim that there _________sufficient evidence to conclude that the population mean is __________than 24.

The College Board provided comparisons of SAT scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. This data set contains verbal SAT scores for a sample of students whose parents are college graduates and a sample of students whose parents are high school graduates. Use 0.01 as your level of significance.

1. Formulate hypotheses to test the research hypothesis. Let population 1 be the students whose parents are college graduates and let population 2 be students whose parents are high school graduates.
2. Is this an one-tailed or two-tailed test?
3. Use Excel to test your hypotheses. What is the test statistic?
4. What is the p-value?
5. What is the critical value?
6. What is your conclusion using 0.01 as the level of significance?
7. Explain your conclusion in the context of the problem (i.e. in terms a non-statistician could understand).

An education minister would like to know whether students at Gedrassi high school on average perform better at English or at Mathematics. Denoting by μ1 the mean score for all Gedrassi students in a standardized English exam and μ2 the mean score for all Gedrassi students in a standardized Mathematics exam, the minister would like to get a 95% confidence interval estimate for the difference between the means: μ1 - μ2.

A study was conducted where many students were given a standardized English exam and a standardized Mathematics exam and their pairs of scores were recorded. Unfortunately, most of the data has been misplaced and the minister only has access to scores for 4 students.

The populations of test scores are assumed to be normally distributed. The minister decides to construct the confidence interval with these 4 pairs of data points. This Student's t distribution table may assist you in answering the following questions.

a)Calculate the lower bound for the confidence interval. Give your answer to 3 decimal places.

Lower bound =

b)Calculate the upper bound for the confidence interval. Give your answer to 3 decimal places.

Upper bound =

An assistant claims that there is no difference between the average English score and the average Math score for a student at Gedrassi high school.

c)Based on the confidence interval the minister constructs, the claim by the assistant can or cannot be ruled out.

• The Assignment must be submitted on Blackboard (WORD format only) via allocated folder.
• Assignments submitted through email will not be accepted.
• Students are advised to make their work clear and well presented, marks may be reduced for poor presentation. This includes filling your information on the cover page.
• Students must mention question number clearly in their answer.
• Late submission will NOT be accepted.
• Avoid plagiarism, the work should be in your own words, copying from students or other resources without proper referencing will result in ZERO marks. No exceptions.
• All answered must be typed using Times New Roman (size 12, double-spaced) font. No pictures containing text will be accepted and will be considered plagiarism).
• Submissions without this cover page will NOT be accepted.

Course Learning Outcomes-Covered

• Employ the skills for managing peoples and other complex issues in technology based organizations. (Lo 2.5)

Question - Develop a hypothetical technological company of your own choice(1) Ikea 2) Nike 3) Seventh Generation 4) Panasonic 5) IBM  6) Unilever 7) Allergan 8) Patagonia 9) Adobe) in any field which follows the concept of ‘Sustainable Development’. Draw an outline of your company’s basic fields of operation and explain how it makes use of various sustainable techniques for its development. (Minimum 3 elements of Sustainable Development should be present in your company’s techniques.)                                                

NOTE:

• It is mandatory for the students to mention their references and sources.
• Students may refer their theoretical course content for the elements of Sustainable Development.
• Word Limit – Minimum 350 words for question.

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a left-tailed test.

This is a two-tailed test.    

This is a right-tailed test.
(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =
(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  
(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    
(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.    

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

A boarding school in your area has asked you to design a simple system so that they could easily identify the students who are staying in the hostel rooms as well as the wardens who are in charge of each student blocks.

Each staff may be in charge of guarding a hostel block. This is not permanent because after certain duration the staff will change blocks. The guarding duty is rotational and not all the staff are required to do this duty. So it is important to keep track of the staff number, staff name and staff contact number as well as the start date and end dates of their guarding duties. The block name and location must also be recorded.

Each hostel block will have many rooms. The room details will be room number and room level. A student can occupy a room but might change rooms in different school terms. A room can be occupied by many students but in different terms. Not all rooms in a hostel block is used for student occupancy. Some rooms are used as store rooms and pantry.

There are many clubs in the school. The clubs are important so that students can enroll in extra co-curricular activities. The school has made it a rule that each student must enroll in at least one club. A club will have many students enrolled as members. The club details will be club name, club established date and the club fee. When a student registers in a club, the date of enrollment must be recorded.

Each student in the school will be assigned under one academic staff. A staff may be in charge of looking after many students. Not all staff are assigned students. The administrative staff will not be assigned any students. Once a student is assigned under the care of a staff, it will be permanent until the day they end their studies in the school. It is very important to know which staff is assigned to which student. Student’s details such as student number, name, name of their guardian as well as the guardian’s contact number must be recorded in case they need to be contacted.

Based on the situation given above, draw a complete Entity Relationship Diagram using the Crow’s Foot notation which includes:

(i)

All entities and attributes

(ii)

Relationships

(iii)

Connectivity and relationship participation

(iv)

Primary and foreign keys

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a left-tailed test.

This is a right-tailed test.    

This is a two-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀     

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.     

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a right-tailed test.

This is a left-tailed test.   

This is a two-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.  

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a two-tailed test.This is a right-tailed test.     This is a left-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not. There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.     We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.We have proven that students who study music in high school have a higher average Math SAT score than those who do not.