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In: Statistics and Probability

A sample on nine public universities and nine private universities was taken. The total cost for...

A sample on nine public universities and nine private universities was taken. The total cost for the year (including room and board) and median SAT score (maximum total is 2400) at each school were recorded. It was felt that schools with higher median SAT scores would have a better reputation and would charge more tuition as a result of that. The data is in the table below. Uss regression to help answer the following questions based on this sample data. Do schools with higher SAT scores charge more in tuition and fees? Are private schools more expensive than public school when SAT scores are taken into consideration.

Category              Total cost                             Median SAT

Public                   21,700                                  1990

Public                   15,600                                   1620

Public                   16,900                                   1810

Public                    15,400                                  1540

Public                    23,100                                   1540

Public                     21,400                                  1600

Public                     16,500                                   1560

Public                     23,500                                   1890

Public                     20,200                                    1620

Private                    30,400                                     1630

Private                    41,500                                    1840

Private                    36,100                                     1980

Private                    42,100                                     1930

Private                     27,100                                    2130

Private                     34,800                                    2010

Private                     32,100                                    1590

Private                     31,800                                    1720

Private                      32,100                                    1770

PLEASE READ: PLEASE SHOW STOP BY STEP HOW YOU GOT THE ANSWER AND PLEASE SHOW HOW TO DO IT STEP BY STEP ON EXCEL. (answer will be thumbed down if this isn't included)

Solutions

Expert Solution

Answer to the question)
The steps are as follows

Enter the data in excel

Click on data tab

Click on data analysis

Select regression from the data analysis window

and click OK , as shown in the image below

.

.

The new window of regression appears on the screen as shown below:

.

.

Enter the Y range as cell addresses for the total cost data

similarly enter the X range as cell addresses for SAT data

[the category data is numbered as 0 for public and 1 for private, so as to convert the data in numerical form]

.

Tick mark the check box of labels if while selecting the x and Y ranage you have mentioned the cell containing the label as well

Then click ok

We get the following output

.

This regression model helps us answer the question if the cost is influenced by the SAT score or not

For this we refer to the test statistic F value and its P value

The F value obtained = 4.53856 with a P value = 0.049 < significance level 0.05

Since the P value < significance level , thsi implies that there is significant evidence that the cost is influence by the SAT score

The coefficient of SAT score is 21.6199

This implies with one unit increase in the SAT score, the increase in the cost is 21.6199 times

it shows a strong positive relatio between the two indicating that higher the SAT score more is the cost

.

Now for the second question are private schools more expensive than the public schools

we can enter the data as follows:

.

In the data analysis window select 2 sample T test assuming unequal variances

click ok

Following window appears on screen:

.

I have entered the private data as variable 1 range

Public cost data as variable 2 range

this will help me to know if Private is more than public or not

tick mark the check box of labels

click ok

The following output appears on screen:

.

The T statistic obtained is positive which implies that Private - public is positive or , in other words, private cost is more than the public cost

The P value of the test is 0.00000156 which is < significance level 0.05

Hence we conclude that yes the cost of private is more than the cost of public and this difference is statistically significant


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