Question Number 05 Two salesmen A and B are working in a certain district. From a sample survey conducted by the Head Office, the following results are obtained as shown in Table 1. State whether there is any significant difference in the average sales between the two salesmen. Assume the populations to be approximately normally distributed with equal variances. Table 1: Comparison of Salesman A and B Salesman A B No. of Samples 20 18 Average Sales (Rs. In Thousands) 175 210 Standard Deviation (Rs. In Thousands) 20 25 The Energy Information Administration gathers data on residential energy consumption and expenditures and publishes its findings in Residential Energy Consumption Survey: Consumption and Expenditures. The independent simple random samples of households in the four U.S. regions yielded the data on last year’s energy consumptions are shown in Table 2. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in last year’s mean energy consumption by households among the four U.S. regions? Table 2: Last year’s energy consumptions for samples of households in the four U.S. regions Northeast Midwest South West 15 17 11 10 10 12 7 12 13 18 9 8 14 13 13 7 13 15 - 9 - 12 - -

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Description: Question Number 05 Two salesmen A and B are working in a certain district. From a sample survey conducted by the Head Office, the following results are obtained as shown in Table 1. State whether there is any significant difference in the average sa

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Question Number 05

Two salesmen A and B are working in a certain district. From a sample survey conducted by the Head Office, the following results are obtained as shown in Table 1. State whether there is any significant difference in the average sales between the two salesmen. Assume the populations to be approximately normally distributed with equal variances.

Table 1: Comparison of Salesman A and B

	Salesman
A	B
No. of Samples	20	18
Average Sales (Rs. In Thousands)	175	210
Standard Deviation (Rs. In Thousands)	20	25

The Energy Information Administration gathers data on residential energy consumption and expenditures and publishes its findings in Residential Energy Consumption Survey: Consumption and Expenditures. The independent simple random samples of households in the four U.S. regions yielded the data on last year’s energy consumptions are shown in Table 2. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in last year’s mean energy consumption by households among the four U.S. regions?

Table 2: Last year’s energy consumptions for samples of households in the four U.S. regions

Northeast	Midwest	South	West
15	17	11	10
10	12	7	12
13	18	9	8
14	13	13	7
13	15	-	9
-	12	-	-

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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