Answer in details for 10marks

Question

(ii) a) 36 out of 100 persons interviewed are familiar with the tax incentives given by the

government for installing solar panels, construct a 96 % traditional confidence

interval for the corresponding true proportion.

b) The average wages of 25 employees of a company are ₹ 2500 with a standard

deviation of ₹ 250. Assuming wages to be normally distributed, calculate 98%

confidence upper bound for the average wages and interpret it.

Answer 1

a) CI = phat +/- z-critical * sqrt(phat * (1-phat)/n)

where phat is sample proportion = 36/100 = 0.36 and n = sample size = 100

Since 96% CI is middle 96% of the area under the normal curve, z-critical for 96% CI is z-score corresponding to 0.98 probability = 2.05.

CI = 0.36 +/- 2.05 * sqrt(0.36*0.64/100)

b) CI = sample mean +/- t-critical * standard deviation/square root(n)

where sample mean = 2500, n = 25, standard deviation = 250

t-critical is t-score corresponding to 0.02 tail probability and n-1 = 24 degrees of freedom = 0.83

CI = 2500 +/- 0.83 * 250/sqrt(25)