STA 3026 Assignment 4- Week 4: Correlation The objectives of this assignment are to help you:

Demonstrate understanding of correlation terminology and its interpretation. Demonstrate how to calculate correlation between two groups of data Calculate confidence intervals

Make quantitative predictions based on linear regression

Construct graphs

In this assignment, you will demonstrate your knowledge of the terms and concepts in Chapter 10 and other previously learned concepts of Even You Can Learn Statistics (EYCLS). Please answer the questions in this file, in the marked boxes.

Be sure to follow these guidelines:

1. Use the concepts from the textbook and notes.

2. Use the Excel calculator for the confidence intervals to construct the intervals for this assignment.

3. In the essay questions, make sure to be clear and thorough. Your answers should be at least 1 paragraph, with 5 complete sentences. 4. Name your file (last name)A4

**Please answer all the questions**.

6 Point values are listed for each question. Deductions as follow:

-1 point for incomplete/partly correct answers

-2 points for incorrect answers

All the points the question is worth will be deducted for blank answers.

**ASSIGNMENT 4 – CORRELATION and CONFIDENCE INTERVALS **

**[Overtype your name in this cell] **

A study about the effect of music on human intelligence sponsored by Musicthatmakesyoudumb.com revealed the

following:

This study was a random sample of schools’ radio station “Top 10” list and the schools’ average SAT scores.

**Music Genre **

Alternative Classic Rock Emo

Hip Hop Jazz

**Number of Schools that have this Genre in their top 10 list **1,679 809

12

10

36

**Average SAT Score **1,152 1,162 1,095 1,104 1,142 1,174 1,097 1,082 1,238 1,113 1,160

Indie 425 Christian 25 Metal 30

Misc 147 Pop 332 Rock 1,881

Source:

http://musicthatmakesyoudumb.virgil.gr/music.php

Count how many music genres there are. Calculate the Mean (Average) SAT Score. In your own words, define Standard Deviation.

2pts 5) In your own words define Statistical Significance (alpha α). 2pts

1) 2) 3)

2pts 2pts

4C) alculate the Standard Deviation for SAT scores.

Given a 95% Level of confidence, what is 2pts the Level of Significance (alpha)?

6) 7)

8)Calculate the Margin of Error (E) for SAT scores

W9)hat is the Upper Limit of the Confidence Interval

What is the Lower Limit of the Confidence Interval

In your own words define Confidence Intervals. (2pts)

10) 11)

2pts 2pts

2pts

In your own words define the Correlation Coefficient (3pts)

12) 13)

Calculate the correlation coefficient R = 3pts

Calculate the regression sum of squares R2

3pts

14)

Based on your calculation of the correlation coefficient what can you conclude? (4pts)

You have been asked by the CEO of your company to develop a measurement to optimize the company’s web site based on the following information. Be sure to do the calculations for all three columns of data.

**Traffic in Number of Visits per Month **

22,314 February 26,789

**Monthly Revenue **

243,898

298,761

389,657 546,792 675,982 786,455 897,645 989,732

**Monthly Cost per Visit **

0.38 0.24 0.21 0.19 0.13 0.11 0.09 0.06

January

March April May June July August

Calculate n = Calculate the Mean =

36,751 48,301 51,329 57,634 63,498 69,045

15)

3pts 3pts 3pts

3pts 3pts 3pts 3pts 3pts

3pts

16)

C17a)lculate the Standard Deviation =

18) Given a 95% Level of confidence, what is the Level of Significance (alpha)?

- 19) Calculate the Margin of Error

- 20) Calculate the Upper Limit

- 21) Calculate the Lower Limit

- 22) Calculate the correlation coefficient between

Traffic in Visits per Month and Monthly Revenue

23) Calculate the correlation coefficient between Visitors per Month and Monthly Cost per Visitor

Traffic in

24) Graph a Scatterplot comparing Monthly Revenue to Visitor Traffic. 4pts

25) Graph a Scatterplot comparing Traffic in Visitors per Month to Cost per Vi4spitt.s

- 26) Based on your calculations, which one has a positive relationship? Explain. (5pts)

- 27) Based on your calculations, would you predict revenue to rise or fall? Explain. (5pts)

- 28) A researcher states that a sequel to a successful movie will also be a success. Explain why this correlation is correct. (5pts)

- 29) A researcher states that games with high levels of difficulty discourage players. Why is this correlation inaccurate? (5pts)

- 30) A publication states that fireworks in a concert increase revenue. Is this a reasonable correlation? Why or why not? (6pts)

- 31) A study reveals that games inhibit critical thinking. Is this a reasonable correlation? Why or why not? (6pts)