A small amount of the trace element selenium, 507200 micrograms (pg) per day. is considered essential to good health. Suppose that random samples of n1 : n2 : 30 adults were selected from two regions of Canada and that a day's intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 1 were ;1 : 167.1 and s1 : 24.9 pg, respectively. The corresponding statistics for the 30 adults from region 2 were ;2 : 140 1 and 52 : 17.8 pg. Find a 95% confidence interval for the difference ([41 r12) in the mean selenium intakes for the two regions. (Round your answers to three decimal places.) E \"a to E \"9 Interpret this interval. 0 95% of all differences will fall within the interval. 0 In repeated sampling, 5% ofall intervals constructed in this manner will enclose the difference in population means. 0 There is a 5% chance that the difference between individual sample means will fall within the interval. 0 In repeated sampling, 95% of all intervals constructed in this manner will enclose the difference in population means. 0 There is a 95% chance that the difference between individual sample means will fall within the interval. In developing a standard for assessing the teaching of pr'ecollege sciences in the United states, an experiment was conducted to evaluate a teacher7developed curriculum, Curriculum A, that was standar'd57hased, activity7oriented, and inquiry7centred. This approach was compared to the historical presentation through lecture, vocabulary, and memorized facts. The perhaps notrsO7startling results when students were tested on concepts are shown in the following table. (Round your answers to three decimal places.) Sample Standard Mean Size Deviation Pretest: All Curriculum A classes 13.33 371 5.51 Pretest: All traditional 14.04 369 5.48 Posttest: All Curriculum A classes 18.8 365 8.02 Posttest: All traditional 16.7 294 6.96 [50 Find a 95% confidence interval for the mean score for the posttest for all Curriculum A Classes. Sta: (h) Find a 95% confidence interval for the mean score for the posttest for' all traditional classes. Em: (c) Find a 95% confidence interval for the difference in mean scores for the posttest Curriculum A classes and the posttest traditional classes. Eta: (d) Does the confidence interval in part (c) provide evrdence that there is a real difference in the posttest Curriculum A and traditional class scores? Explain. 0 Since the value .111 7 p2 = O is not in the confidence interval, it is likely that there is a difference in the population means. 0 Since the value pl p2 : O is in the confidence interval, it is likely that there is a difference in the population means. O Since the value \"1 7 p2 : O is in the confidence interval, it is not likely that there is a difference in the population means. 0 Since the value .111 7 p2 = O is not in the confidence interval, it is not likely that there is a difference in the population means. Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table. Hotel A Hotel B Hotel C Sample average ($) 150 160 110 Sample standard deviation 17.2 22.1 12.3 (a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.) to $ (b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.) $ to $Independent random samples of n, = 800 and n, = 670 observations were selected from binomial populations 1 and 2, and x, = 337 and x, = 371 successes were observed. LA USE SALT (a) Find a 90% confidence interval for the difference (p, - p2) in the two population proportions. (Round your answers to three decimal places.) to