Mathematical Statistics 2019/2020, Homework 7
Name and Surname ... Student’s number ...
In the problems below, please use the following: as k – the sum of digits in your student’s number; as m – the sum of the two largest digits in your student’s number;
and as n – the smallest digit in your student’s number plus 1. For example, if an index number is 609999: k = 42, m = 18, n = 1.
Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in decimal notation, rounded to four digits).
7. The coronavirus pandemic affected individual expenditures on food; a researcher studies the decrease (in $) of weekly expenditures for a random sample of 5n individuals. Assuming that the decrease (in $) follows a normal distribution, find the (80 −52n2+252n)% confidence interval for the average decrease of weekly food expenditures and the (105 +52n2−252n)% confidence interval for the variance of the decrease of weekly food expenditures, knowing that in the studied sample, the average decrease amounted to $10m, and the variance of the decrease (unbiased estimator) amounted to k2. How many more respondents should be interrogated in order to obtain a confidence interval for the average decrease of length not exceeding m (in $) for the whole sample (in Stein’s procedure)?
ANSWER:
CI for mean: CI for variance: additional number:
Solution:
