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# Constructing a CI for a price index

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1i. Construct a 95% confidence interval.

= 12
S = 3.19
n = 11
α = .05
= 0.96

A. Determine the t Value:

1. Significance level = .05
2. Degrees of Freedom (df)
df = n-1
df = 11 - 1
df = 10
3. Determine the t value from the t Table
t value = 2.228

B. 95% confidence interval:
±
12 ± 2.228(0.96)
12 ± 2.14
95% confidence interval: 9.86 and 14.14

MODERN FIXTURES

In 19x9, you are estimating a should-pay price for 500 fixtures as part of a building modernization. An offeror has proposed a price of \$100,125.

You have the data in the table from five previous buys in which the price paid was considered fair and reasonable.

YEAR QUANTITY UNIT PRICE TOTAL PRICE
19X4 150 \$164.85 \$24,728
19X5 145 \$163.20 \$23.664
19X6 150 \$171.30 \$25.695
19X7 165 \$181.80 \$29.997
19X8 140 \$190.50 \$26,670

Given that the following index applies to this contracting situation, would you consider the Price to be fair and reasonable?

YEAR INDEX
19X4 109.9
19X5 108.8
19X6 114.2
19X7 121.2
19X8 127.0
19X9 133.5*

*Current estimates for 19x9

PRICE INDEX EXERCISE NUMBER 2

1. Given the following contract information, calculate the adjusted contract price:

Contract Value \$400,000
Base Index 124.5
Index at Delivery 132

2. Given the following contract information, calculate the adjusted contract price.

Contract Value \$550,000
Base Index 125.5
Index at Delivery 132.7

PRICE INDEX EXERCISE NUMBER 3

1. The price of an item was \$200 in 19X4 and \$220 in 10X5. Calculate a simple price index for this item using 19X4 as the base year.

2. You are searching for a Government price index to use in estimating the price of an industrial chemical product. You have price data from 12 months ago. Would the Consumer Price Index (CPI) or a Producer Price Index (PPI) be the better choice for you to use? Why?

3. An item cost \$250 each 8 months ago. The relevent index was 110.0 at that time. Today the index is 115.5. Estimate the item's price today.

4. A \$400,000 fixed price EPA contract contains a provision requiring an adjustment for 10% of the contract price based on changes in the index identified in the contract. That index at the time of contract award was 124.5. At the time of delivery the index was 132.0. What is the final contract price?

5. A \$500,000 fixed price economic price adjustment contract contains a provision requiring an adjustment for 20 percent of the contract price based on changes in the index identified in the contract. The index at the time of contract award was 120.0. At the time of delivery the index was 132.0. What is the final contract price?