Discuss the below:
Q1. a. Define the term consistency in the context of a desirable property for an estimator.
b. A farmer selected a random sample of 60 cows from his farm and weighed the milk produced for each cow in the sample. This sample yielded a sample mean of 45.2 pounds per day and a sample standard deviation s = 16.45 pounds.
i. Compute the 95% confidence interval for the population mean weight of the milk produced by the cows.
ii. Test the hypothesis that the population weight of cows' milk is 50 pounds.
Q2. A study conducted by the Ministry of National Security on missing children in Caribbean island state includes a sample of 95 boys and 200 girls taken from a from a database maintained by the Crime and Problem Analysis Branch of the Police Department. The boys sample showed that 75 of them return home, while the girls sample showed that 125 of them return home after a missing person report has been made.
a. Define the term point estimate for the difference of two means.
b. Determine whether the point estimator