1. The following data were obtained in a study of the relationship between the weight and chest size of infants at birth: Weight (kg) 2.75 Chest size (cm) 29.5 2.15 26.3 4,41 32.2 36.5 5.52 3.21 27.2...

Engineering Data Analysis Answer 2) a, b, c

Extracted text: 1. The following data were obtained in a study of the relationship between the weight and chest size of infants at birth: Weight (kg) 2.75 Chest size (cm) 29.5 2.15 26.3 4,41 32.2 36.5 5.52 3.21 27.2 4.32 27.7 231 26.3 4.30 30.3 3.71 26.7 a. Validate the claim that the weight of the infant has influence on its chest size by testing the linear correlation between the two variables. b. If there is a linear correlation, based on your computation in letter (a), construct a simpie linear regression model. Otherwise, disregard this question and the next question. e Estimate the chest size given that the weight is 3.00 kg. 2. To monitor the acid mine pollution from Philsaga Mining Corporation, two independent sampling stations were chosen. One located downstream from the acid mine discharge point and the other located upstream. For 12 monthly samples collected at the downstream station the species diversity index had a mean value of 3.11 and a standard deviation of 0.771, while 10 monthly samples collected at the upstream station had a mean index value 2.04 and a standard deviation of 0.448. a. What is the value of point estimate? b. Find a 90% confidence interval for the difference between the population imeans for the two locations, assuming that the populations are approximately normally distributed, C. Test the hypathesis that there is no difference between the means using 0.05 level of significance. (Hint: Test the hypothesis of variance first) 3. A certain change in a process for manufacture of component parts is being considered. Samples are taken using both the existing and the new procedure so as to determine if the new process results in an improvement. If 75 of 1500 items from the existing procedure were found to be defective and 80 of 2000 items from the new procedure were found to be defective, a. What is the value of the point estimate? b. Find a 90% confidence interval for the true difference in the fraction of defectives between the existing and the new process. c. ALO.05 level of significance, test the hypothesis that the new procedure is much better than the existing one.