QA 233 (Basic Business Statistics)

Practice Problems X - Chapter 12

Hello QA 233 students! The following problems require you to use material from 'Regression Analysis'(slide set 10 and chapter 12 in the ASW textbook). I have also posted the solutions on the Virtual Classroom web page. Have a good day.

1. Dee Zerta is the proprietor of Ice Dreams, a local chain of ice cream soda shops. Ms. Zerta frequently has difficulty estimating her shop’s daily demand, which in turn has lead to problems with her inventory. Because vanilla ice cream is the basis for so many of Ice Dreams’ menu items (such as banana splits, parfaits, sundaes, shakes and malts), anticipation of demand for this flavor is her greatest challenge. However, Ms. Zerta has noticed that her sales seem to increase as the outside temperature increases, and she believes she may be able to use this knowledge to alleviate this problem. She randomly selects twenty days from the previous year and uses the internet to find the official high temperature in her area for those days. She then uses her business records to find the amount of vanilla ice cream sold by the Ice Dreams shops on those days. Her results are given below.

    

   Date	Gallons of Vanilla Ice Cream Sold	Official High Temperature
   11-01-00	151	64°
   03-11-00	98	58°
   05-19-00	233	82°
   01-30-00	61	48°
   12-14-99	58	54°
   04-14-00	201	75°
   06-22-00	311	93°
   06-07-00	322	89°
   02-08-00	164	61°
   11-19-99	111	57°
   10-22-00	192	78°
   05-22-00	275	90°
   09-09-00	345	99°
   03-28-00	221	71°
   06-25-00	391	103°
   07-02-00	382	98°
   10-29-00	168	77°
   08-19-00	363	101°
   08-02-00	370	97°
   04-22-00	215	80°

   Please use these data to help Ms. Zerta determine the relationship between outside temperature and sales of vanilla ice cream at her shops.

2. George Steinbrenner, the owner of the New York Yankees, is arguing with other about whether a baseball team’s attendance is related to how successful the fans expect the team to be. In an attempt to make his point, Mr. Steinbrenner has one of his staff members assemble data on the Yankees total attendance during each season from 1976 through 1990. He also has the staff member record the number of wins the Yankees had achieved during the previous season for each of these seasons. The data are:

   Season	Attendance (in millions of fans)	Wins During Previous Season
   1976	2.0	83
   1977	2.1	97
   1978	2.3	100
   1979	2.5	100
   1980	2.6	89
   1981	2.4	103
   1982	***	***
   1983	2.3	79
   1984	1.8	91
   1985	2.2	87
   1986	2.3	97
   1987	2.4	90
   1988	2.6	89
   1989	2.2	85
   1990	2.0	74

   Mr. Steinbrenner’s assistant recognized that approximately one-third of the 1982 season was cancelled due to a player’s strike, and so has omitted that season from the data. Please use the data collected to determine if Mr. Steinbrenner has a supportable conjecture with regards to the Yankees. Also explain for Mr. Steinbrenner the nature of the relationship between the Yankees’ attendance and their level of success on the field during the previous season.

3. Johnny Bravo, ace QA 233 student, wants to demonstrate the relationship between the number of hours a student spends studying and the grades that he/she earns. He randomly selects ten students and asks them to record the number of hours they spend studying throughout the quarter. After the quarter has concluded he also records the GPA each student earned during the quarter. His results follow:

Student ID Number	Total Hours Spent Studying During the Quarter	Grade Point Average
2196	153	3.75
2907	122	3.15
3108	97	2.40
2562	182	4.00
4680	115	2.33
1741	75	1.80
0850	104	2.50
9123	119	2.90
3408	98	2.50
2597	122	2.85

 Please use the data collected by Johnny to determine the nature of the relationship between the number of hours a student spends studying and the grades that he/she earns.

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