Question

Question Two a) Given the following data of five commodities: Commodity Base Year Current year Value Quantity Value Quantity 72 12 12 80 84 80 20 56 30 764 (0 Calculate Laspyre's, Kelly's and Fischer's Quantity Indices Demonstrate how the Fischer's Price Index satisfies both the reversal and factor reversal tests. The weight of full boxes of a certain type of cerealis normally distributed with a standard deviation of 28 grams. A sample of 42 randomly selected boxes gave a mean of 430 grams b) Construct a 95% confidence interval for the whole population of this type of cereals. () Suppose the sample size is increased to 74 boxes, what happens to the confidence evel? D e嬲自の四個@M

Answer 1

a)

(i)

Laspeyres’ quantity index:

Q₀₁ =$(\Sigma q1/\Sigma q0)*100$ =[(12+... +8)/(10+...+7)]*100 =(42/42)*100 =100

Kelly's quantity index:

Q₀₁ =$(\Sigma\ q1.p/\Sigma\ q0.p)*100$ =[(12*72+...+8*64)/(10*72+...7*64)]*100

(Here, p is p1. We can also use p0)

Fischer's quantity index:

Q₀₁ =$\sqrt{(\Sigma\ q1.p0/\ \Sigma\ q0.p0)*(\Sigma\\ q1.p1/\Sigma\ qo. p1)} *100$

b)

(i)

95% confidence interval for population mean, $\mu$ =$\bar{X} \pm( Z. \sigma/\sqrt{n})$ =$430 \pm( 1.96(28)/\sqrt{42})$ =(421.532, 438.468)

(ii)

If sample size, n is increased to 74, the 95% confidence interval wiil be (423.620, 436.380), that is, increase of sample size lead to decrease in the width of confidence interval.

So, if n increases, nothing happens to the confidence level. We can choose any confidence level like 95%, 99% or 90%, etc,.