A random sample of 14 chemical solutions is obtained, and their strengths are measured. The sample mean is 5437.2 and the sample standard deviation is 376.9. (a) Construct a two-sided 95% confidence interval for the average strength.
(b) Estimate how many additional chemical solutions need to be measured in order to obtain a two-sided 95% confidence interval for the average strength with a length no larger than 300.

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?