List of top Statistics for Economics Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

Let 𝜋 be the proportion of a population vaccinated against a disease. An estimate ̂𝜋 = 0.64 is found using a sample of 100 individuals from the population. The 𝑧 test statistic for the null hypothesis 𝐻₀ : 𝜋 = 0.58 is ________ (round off to 2 decimal places).

Let 𝑌 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(3, 1), 𝑊 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(1, 2) and 𝑋 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 (𝑝 = 0.9) where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = 𝑋𝑌 + (1 − 𝑋)𝑊. Then 𝐸(𝑆) = _________ (round off to 1 decimal place)

If 𝑋 denotes the sum of the numbers appearing on a throw of two fair six-faced dice then the probability
𝑃( 7 < 𝑋 < 10) = ______ (round off to 2 decimal places).

The portfolio of an investment firm comprises of two risky assets, 𝑆 and 𝑇, whose returns are denoted by random variables 𝑅_𝑠 and 𝑅_𝑇 respectively. The mean, the variance and the covariance of the returns are
𝐸(𝑅_𝑠 ) = 0.08, 𝑉𝑎𝑟(𝑅_𝑠 ) = 0.07, 
𝐸(𝑅_𝑇 ) = 0.05, 𝑉𝑎𝑟(𝑅_𝑇 ) = 0.05, 𝐶𝑜𝑣(𝑅𝑠 , 𝑅_𝑇 ) = 0.04. 
Let 𝑤 be the proportion of assets allotted to 𝑆 so that the return from the portfolio is 𝑅 = 𝑤𝑅_𝑠 + (1 − 𝑤)𝑅_𝑇 . The value of 𝑤 which minimizes 𝑉𝑎𝑟(𝑅) is _____(round off to 2 decimal places)

A number 𝑥 is randomly chosen from the set of the first 100 natural numbers. The probability that 𝑥 satisfies the condition \(𝑥 + \frac{300}{𝑥} > 65\) is ______ (round off to 2 decimal places).

Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅² = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).