(6 marks 2. A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood haemoglobin levels (grams per deciliter (g/dl)) at 12 months of age: Group Sample size Sample mean (g/dl) sample standard deviation (g/dl) Breast-fed 36 17.3 2 Formula 49 16.4 3 (a) (b) Test if the mean hemoglobin level is higher among breast-fed babies. Use the 1% significance level. (8 marks) Obtain a two-sided 99% confidence interval for the mean difference between the two populations of infants. (4 marks) 3. R. Sitchler et al. compared two methods of measuring treadwear in their paper "Measurement of Treadwear of Commercial Tires" (Rubber Age, Vol. 73:2). Eleven randomly chosen tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The data, in thousands of miles, are as follows. Weight Groove Weight Groove method method method method 30.5 28.7 24.5 16.1 30.9 25.9 20.9 19.9 31.9 23.3 18.9 15.2 30.4 23.1 13.7 11.5 27.3 23.7 11.4 11.2 20.4 20.9 (a) Why are these data best regarded as a paired sample? (2 marks) 2 STAT 151 Assignment 5 (b) Do the data provide evidence that on average, the two measurement methods give different results? Test at the 10% level of significance (8 marks) (c) Construct and interpret a 95% confidence interval for the mean difference in the results of the two measurement methods. (6 marks) (d) The following plots display the sample distribution of paired differences (weight method - Groove method). Do the plots provide any clear indication against the assumption of a normally distributed population? Explain. (2 marks) O Plot