Statistics - Hypothesis Testing Projects

: The mean family income is $31,500, with a standard deviation of $4,000. Assuming a normal distribution,

# 3 : The mean family income is $31,500, with a standard deviation of $4,000. Assuming a normal distribution, what exactly would that tell you about the incomes of Flint people? Be specific with a precise statistical answer!!!

#4 : Assume you have collected data on actual incomes from people using a random sampling method. You collect the following 25 observations.
a. Is the data normally distributed - or even close?
c. Using the S.E. Mean, generate a 95% CI around the mean. What does this range tell you?

Raw data
28.00, 11.00, 10.00, 72.00, 36.00, 29.00, 25.00, 56.00, 17.00, 33.00, 23.00, 18.00, 19.00, 22.00, 8.00, 72.00, 25.00, 32.00, 31.00, 26.00, 28.00, 43.00, 18.00, 12.00, 19.00

Andy's Ice Cream Shop is located in a very warm part of Texas. You collect data about the number of gallons of ice cream sold and the temperature outside (in Celsius):

Day	Ice Cream Sales (gallons)	Ave Temp (C)

1	100	10
2	132	15
3	140	20
4	213	24
5	180	21
6	75	8
7	160	18
8	150	17
9	185	22
10	160	21

Which variable is dependent and which variable is independent?
Articulate a plausible explanation for why these two variables could be related. Hint: try common sense!
Which correlation coefficient (Spearman Rho or Pearson) would you use for this problem? Why?
Calculate a correlation coefficient. (Hint: See Norusis, page 486-487).
Perform a simple linear regression. What is the resulting equation? What is the R squared? (Hint: Norusis, p. 441-449)
Say it is 18 degrees Celsius. How many gallons of ice cream do you think you will sell? (Hint: make use of the regression coefficients as shown on page 449 of Norusis)

2. Andy is a cooperative student with Perkins Institute, a highly selective cooperative engineering and management college. At this school students spend alternate periods of school and work. His boss has asked him to examine the relationship between incoming students' ACT (American College Testing) scores (note: these range from 12 to 32) and their high school GPA and their ultimate college GPA (on a 4.0 scale) and average work performance evaluation (on a 4.0 scale) they earn while at Perkins. Andy's boss pleads "Help me determine who to accept! I can't stand to see folks fail in this program. It costs me too much. Success means both earning good college grades and working well in the company. How can I predict success in these two areas, given the information I have to work with - namely, HS GPA and ACT score?" Note that College GPAs of under 2.0 are failing and under 2.5 are weak. Also note that work evaluation averages below 3.0 are weak. If this problem and the data seem a bit vague - they are. Unfortunately, real world data is rarely clear and unambiguous!

Assume that the following data is representative of what Perkins experiences with hundreds of new students.

Student	ACT	HS GPA	College GPA	Work Eval

1	24	3.4	2.1	3.3
2	28	3.7	3.2	3.7
3	29	3.9	4.00	3.0
4	31	3.5	3.50	3.7
5	30	3.2	3.10	3.0
6	29	4.0	3.95	3.3
7	30	3.6	3.70	2.8
8	28	3.8	3.60	3.8
9	23	3.2	2.90	3.6
10	28	2.9	3.20	3.0
11	20	3.7	1.95	2.2
12	19	3.3	2.70	4.0

Use SPSS to graph the relationships between the following pairs of variables: ACT and College GPA, HS GPA and College GPA, HS GPA and Work Eval and ACT and Work EVAL. In words what do the graphs reveal? Is there a pattern (perhaps positively or negatively sloped)? (Hint: I would suggest running a scatter plot)
Calculate a correlation coefficient matrix for the four variables. (hint: use the Bivariate Correlation procedure shown on page 486-487 of Norusis).
What conclusions would you draw from this data? What would you encourage Andy's boss to do? Remember, he knows a potential student’s HS GPA and ACT. He wants to predict their success in college (College GPA) and success in work (Work Evaluation).

3. John Herr is an analyst for the Best Foods grocery chain. The firm operates four grocery stores. John is interested in knowing if the average dollar amount per purchase is identical for the four stores. John randomly selected six receipts from each of the four stores:

Store 1	Store 2	Store 3	Store 4

13.05	16.17	9.48	9.52
23.94	18.52	6.92	10.92
14.63	19.57	10.47	11.12
25.78	21.40	7.63	9.32
17.52	13.59	11.90	12.73
18.45	20.57	9.92	8.92

Use SPSS to perform an ANOVA on this data.
What are the null and alternative hypotheses?
Is there support in this data for the notion that average dollar amount per purchase is the same for all stores?

Price: $14.61

Solution: The downloadable solution consists of 12 pages, 261 words and 14 charts.
Deliverable: Word Document