1. Calculate a 95% confidence interval (CI) on the average weight of packaged mustard seed. Explain very carefully to the packaging workers what the 95% confidence interval numbers mean. Include your SPSS output. (1 points)
2. Now, let's assume that the package claims that it contains 1.7 oz. of mustard seed. Some of the customers claim that there isn't enough mustard seed in the 1.7 oz. economy size; corporate management is worried that there may be too much. Given the sample of 36, assuming that it is adequate, test the hypothesis that the average amount of mustard seed in the package meets the 1.7 oz. standard with, say, 95% confidence. Be sure to state the null and alternative hypothesis and which you support. Include your SPSS output. (2 points)
3. Over a period of time, Juan determines that the true mean of the packages is in fact 1.72 ounces with standard deviation the same as the sample above. Assume that Juan has a strong consumer orientation. Juan is also a savvy businessman. Indeed, a local TV station has been checking up on Juan by periodically sampling 36 packages and figuring up the average weight. Juan tells you that he wants to be at least 95% sure that the average package has at least 1.7 ounces. Further, he wants to be sure that 95% of the time, the TV crew that is watching him will find a sample mean of at least 1.70 ounces. At the same time he doesn't want to set the equipment to fill packages with any more product than he absolutely has to. What advice would you give the mustard seed packaging factory management as to how to calibrate their equipment? In particular, should they increase or decrease the amount they are putting in the packages? Are there any other steps they might be able to take to improve the situation? (1 point)

Chi-square

Please post your response to this problem to the assignment area along with your Stats 2 - Juan Valdez solution by day 7 of seminar 4. The Valdez problem will weigh in at 4 pts while this assignment will weigh 2 pts.

A market research firm conducts a brand awareness test on a new product. As marketing manager you suspect there is a difference between the awareness levels of males and females. To test this out you conduct a quick market research test of 100 respondents. You find:

Dataset - 69 respondents - 35 men and 34 women are aware of the product. You also find that 31 respondents - 25 men and 6 women are not aware of the product.

Based on lecture you can use the ANALYZE, DESCRIPTIVE and the CROSSTABS option to see if there is a statistical difference between male and female brand awareness. Alternatively, you can follow Norusis chapter 17 (however, the answers may vary a little). What are your hypotheses (H0 and H1)? With 95% confidence, which do you support?  What is the chi-square statistic? What is the probability value (labeled "significance" by SPSS)? Interpret this result. Be sure to include some of your SPSS output in your answer.

Hint: You may need to do a bit of keying here - perhaps 100 rows of data with two columns (gender and aware)? You could calculate the chi-square stat using the formula in chapter 17 - but you would not get the significance values.

Hint: In chi-square problems, H0: variables are independent, H1: variables are dependent

Please complete each one of the following three questions.

Please submit using the assignment link by day 5 of seminar 5. Material in Norusis chapter 15 and 19-21 may be helpful.

1. 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):

1. Which variable is dependent and which variable is independent?
2. Articulate a plausible explanation for why these two variables could be related. Hint: try common sense!
3. Which correlation coefficient would you use for this problem? Why?
4. Calculate a correlation coefficient.
5. Perform a simple linear regression. What is the resulting equation? What is the R squared? f. Say it is 17 degrees Celsius. How many gallons of ice cream do you think you will sell?

Check Figures - R squared about .9, F ratio > 70, slope is around 7 and intercept is around 25 or so.

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.  In working the problem don’t focus on individual students in this dataset.

1. 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)
2. Calculate a correlation coefficient matrix for the four variables. (hint: use the Bivariate Correlation procedure shown at the end of chapter 21 of Norusis).
3. 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).

NOTE: This problem employs fictitious data. It is based, however, on a real experience the author had several years ago.

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:

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

Hint: You cannot enter this data as four columns. Instead enter the data in two columns: Store number (1, 2, 3 or 4) and Sales (13.05, 5.48. etc.). Think about which column is a "dependent" variable and which is a "factor".  Chapter 15 in Norusis should serve as a guide.