## Business Statistics (1430) Spring 2012 AIOU assignment

Course: Business Statistics (1430) Semester: Spring, 2012

Level: B.A/B.Com/BBA Total Marks: 100

ASSIGNMENT No. 1
(Units: 1-4)

Q.1 The Bureau of Labor Statistics has sampled 30 communities’ nationwide and compiled prices in each community at the beginning and end of August in order to find out approximately how the Consumer Price Index (CPI) has changed during August. The percentage changes in prices for the 30 communities are as follows:

0.7 0.4 -0.3 0.2 -0.1 0.1 0.3 0.7 0.0 -0.4
0.1 0.5 0.2 0.3 1.0 -0.3 0.0 0.2 0.5 0.1
-0.5 -0.3 0.1 0.5 0.4 0.0 0.2 0.3 0.5 0.4

(a) Arrange the data in an array from lowest to highest. (5)
(b) Construct a frequency distribution using an appropriate class interval. (8)
(c) How many communities had prices that either did not change or that increased less than 1.0 percent? (5)
(d) Are these data discrete or continuous? (2)

Q.2 Hypothetical data from a Hospital have the following frequency distribution representing weight in pounds at birth of 200 premature babies.

Class Frequency Class Frequency
0.5-0.9 10 2.5-2.9 29
1.0-1.4 19 3.0-3.4 34
1.5-1.9 24 3.5-3.9 40
2.0-2.4 27 4.0-4.4 17

Construct an ogive that will help you answer the following questions:
(a) What was the approximate middle value in the original data set? (10)
(b) If premature babies less than 3.0 pounds are normally kept in an incubator for several days as a precaution, about what percentage of Central’s premature babies will need an incubator? (10)
Q.3 The ages of residents of Twin Lakes Retirement town have the following frequency distribution:
Class Frequency
47-51.9 4
52-56.9 9
57-61.9 13
62-66.9 42
67-71.9 39
72-76.9 20
77-81.9 9 (5+5+5+5)

Estimate the modal value, 50th percentile, quartiles and coefficient of skewness of the distribution

Q.4 There are a number of possible measures of sales performance including how consistent a sales person is in meeting established sales goals. The following data represent the percentage of goal met by each of three salespeople over the last 5 years.
Mr. A 76 68 89 92 104
Mr. B 79 88 90 86 81
Mr. C 114 88 118 88 121

(a) Which salesperson is the most consistent? (15)
(b) Comment on the adequacy of using a measure of consistency along with percentage of sales goal met to evaluate sales performance. (5)

Q.5 Here are the ages in years of the Honda motor cycles worked on by the Village Autohaus last week:
5 6 3 6 11 7 9 10 2 4 10 6 2 1 5

(a) Compute the mode for this data set.
(b) Compute the mean of the data set.
(c) Compare parts (a) and (b) and comment on which is the better measure of the central tendency of the data.
(d) Define the following terms.
Statistical inference, Estimation, Testing of Hypothesis, P-value, confidence interval (5+5+5+5)

ASSIGNMENT No. 2
(Units: 4–7) Total Marks: 100

Q.1 (a) Define the following terms:
Null hypothesis, Alternative hypothesis, test statistics, Level of significance, type-I error, type-II error, power of the test, parameter, statistic, acceptance region. (10)
(b) Jhon Douglas, the new manager Food Barn, is interested in the percentage of customers who are totally satisfied with the store. The previous manager had 86 percent of the customers totally satisfied, and Jhon claims the same is true today. Jhon sampled 187 customers and found 157 were totally satisfied at the 1% level of significance, is there evidence that Jhon’s claim is valid? (10)

Q.2 (a) A television documentary on overeating claimed that Americans are about 10 pounds overweight on the average. To test this claim, eighteen randomly selected individuals were examined; their average excess weight was found to be 12.4 pounds, and the sample standard deviation was 2.7 pounds at a significance level of 0.01, is there any reason to doubt the validity of the claimed 10-pound value? (10)
(b) Two research laboratories have independently produced drugs that provide relief to arthritis sufferers. The first drug was tested on a group of 90 arthritis sufferers and produced an average of 8.5 hours. The second drug was tested on 80 arthritis sufferers, producing an average of 7.9 hours of relief, and a sample standard deviation of 2.1 hours. At the 0.05 level of significance, does the second drug provide a significantly shorter period of relief? (10)

Q.3 (a) Citizen Health Club has been advertising a rigorous program for body conditioning. The club claims that after 1 month in the program, the average participant should be able to do eight more push-ups in 2 minutes than he or she could do at the start. Does the random sample of 10 program participants given below support the club’s claim? Use the 0.05 level of significance. (10)

Participant 1 2 3 4 5 6 7 8 9 10

Before 38 11 34 25 17 38 12 27 32 29

After 45 24 41 39 30 44 30 39 40 41

(b) Two different areas of a large eastern city are being considered as sites for day-care centers. Of 200 household surveyed in one section, the proportion in which the mother worked full-time was 0.52. In another section, 40 percent of the 150 households surveyed had mothers working at full time jobs. At the 0.04 level of significance, is there a significant difference in the proportion of working mothers in the two areas of the city? (10)
Q.4 For the following data set:
X 13 16 14 11 17 9 13 17 18 12
Y 6.2 8.6 7.2 4.5 9.0 3.5 6.5 9.3 9.5 5.7

(a) Plot the scatter diagram. (7)
(b) Calculate the sample coefficient of correlation and the sample of coefficient of determination. (13)

Q.5 Pepsi Cola is studying the effect of its latest advertising campaign. People chosen at random were called and asked how many cans of Pepsi Cola they had bought in the past week and how many Pepsi Cola advertisements they had either read or seen in the past week.

[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image002.gif[/IMG] 3 7 4 2 0 4 1 2
[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image004.gif[/IMG] 11 18 9 4 7 6 3 8

(a) Fit and interpret the equation Y= a+bx. (10)
(b) Mr. Bill owner of an Indian vineyard has collected the following information describing the prices and quantities of harvested crops for the years 1992-1995.

Price \$ (Per tons) Quantity Harvested (tons)

Type of Grape 1992 1993 1994 1995 1992 1993 1994 1995

Ruby Cabernet 108 109 113 111 1.280 1.150 1.330 1.360

Barbera 93 96 96 101 830 860 850 890

Chenin Balance 97 99 106 107 1.140 1.760 1.630 1.660

Construct a Laspeyres index for each of these 4 years using 1992 as the base
period. (10)