For all problems on this page, use the following setup: Let N be a positive integer random variable with PMF of the form pN(n)=12⋅n⋅2−n, n=1,2,…. Once we see the numerical value of N , we then draw a random variable K whose (conditional) PMF is uniform on the set {1,2,…,2n} . Joint PMF 1 point possible (graded, results hidden) Write down an expression for the joint PMF pN, K(n, k) . For n=1,2,… and k=1,2,…,2n : pN, K(n, k)=

Amanufacturing firm has been averaging 16.8 orders per week for several years. however, during a recession, orders appeared to slow. suppose the firm’s production manager randomly samples 31 weeks and finds an average of 15.6 orders with a standard deviation of 2.3 orders. using a 0.025 significance level, test whether the mean number of orders has decreased. type the full 5 step procedure into the answer box, then for multiple choice practice, answer the following: 1. what is the name and symbol of the parameter that you are testing? 2. what is the symbol and value of the point estimate of that parameter? 3. what distribution are you using to test this parameter? 4. what is the critical value? 5. what is the test statistic value? 6. what is the p-value?