Sample problem section from a previous final exam

1. Duke is in charge of filling milk bottles at the local dairy. His boss Amy wants to assess the consistency of fill in the bottles by drawing a sample of the bottles. She wants to be 90% confident that her sample is representative. She will allow error of .12 ounces, and from past tests she expects standard deviation of about .03 ounces. How many bottles should Duke draw for Amy's test? Show all work for credit.

2. Slushee Company is trying to find out what percent of its customers like the strawberry-kiwi flavor of its patented frozen treat. A similar study last year found that about 65% did. Alan Slushee, the company CEO, want to be 99% sure of his result, and is willing to live with 5% error. How many customers should he survey?

3. Coca-Cola is developing a new fruit-flavored soft drink, and is testing various sweetness levels for the new product. A market test of four sweetness levels resulted in the following data:

Sweetness Level Subjects Preferring
Low 11
Moderately low 21
Moderately high 37
High 31

Is there a significant preference among the sweetness levels at the .05 level? (25) note: Dcrit = 1.36/(n)1/2

3. A cross tabulation of the frequency of visits per month to a convenience store by sex is given in the table below. Conduct a chi-square test to determine whether there is a relationship between sex and the frequency of visits, at the .05 level of significance. (25 points)

Frequency of Visits Male Female Totals
1-5 14 26 40
6-14 16 34 50
15 and above 15 11 26
totals 45 71 116

4. Suzy, CEO of Ajax conglomerate, has been investigating the relationship between advertising (X in thousands of dollars) and sales of Ajax garters (Y in thousands of shipped units). Her data looks like this for the last four quarters:
qtr ad sale ad2 sales2 ad X sales
1 400 3,200 160,000 10,240,000 1,280,000
2 510 6,700 260,100 448,900,000 3,417,000
3 320 3,020 102,400 9,120,400 966,400
4 280 2,890 78,400 8,352,100 809,200
sum 1,510 15,810 600,900 72,602,500 6,472,600
avg 377.5 3,952.5 150,225 18,150,625 1,618,150

  1. Compute and interpret the correlation between advertising and sales. (20 points)
  2. Estimate the regression function, and explain the meaning of the function. (20 points)

5. Ajax wants to know if there is a statistical difference in effectiveness between three advertising campaigns. Perception scores for the three ad campaigns A, B, and C (scored on a 0-200 scale, 200 points being highest level of perception) were collected and processed. Sam in the research department has plugged the numbers into a statistics package, but the computer shut down before giving the final answer. Take what's left below and answer the question for Ajax, TESTING FOR SIGNIFICANCE AT THE 0.05 LEVEL. (20 points)

Campaign A: 25 subjects rating

Campaign B: 25 subjects rating

Campaign C: 25 subjects rating

SSA = 10 SSE = 63.6