Confident Interval

Fall 2012 Assignment 5 (Total Points Possible 15) Name waft ID Instructions Use this page as your cover page, and attach your groupwork git your work. Your assignment answers should be in complete and grammatically correct sentences. 1. tally to the National Center for Health Statistics (2004), 22. 4% of adults are smokers. A ergodic attempt of 300 adults is obtained. (a) Describe the take distribution of phat, the sample parity of adults who smoke. (b) In a haphazard sample of 300 adults, what is the probability that at least 50 are smokers? c) Would it be unusual if a random sample of 300 adults results in 18% or less be smokers? Explain your answer.2. A gondola at K&A resistance & Manufacturing Company produces a certain copper tubing component in a refrigeration unit. The tubing components produced by the manufacturer consume a hateful diameter of 0. 75 butt against with a standard expiration of 0. 004 inch. The quality-control inspector takes a random sample of 30 components once apiece week and calculates the average diameter of these components. If the mean is either less than 0. 748 inch or greater than 0. 752 inch, the inspector concludes that the machine needs an adjustment. a) Describe the sampling distribution of the sample mean diameter for a random sample of 30 such components. (b) What is the probability that, based on a random sample of 30 such components, the inspector will conclude that the machine needs an adjustment when, in fact, the machine is correctly calibrated?3. In a random sample of 678 adult males 20 to 34 age of age, it was findd that 58 of them suck up hypertension (high blood pressure). Source The Centers for affection Control. (a) Obtain a window pane estimate for the proportion of adult males 20 to 34 years of age who switch hypertension. b) Construct a 95% sureness interval for the proportion of adult males 20 to 34 who have hypertension. Interpret the faith interval. You wish to conduct your own study to determine the proportion of adult males 20 to 34 years old who have hypertension. (c) What sample size of it would be unavoidable for the estimate to be deep down 3 percentage points (interval duration is 0. 06) with 95% confidence if you use the point estimate obtained in part (a)? (d) What sample size would be needed for the estimate to be within 3 percentage points with 95% confidence if you dont have a prior estimate (use phat=. )? 4. A random sample of 60 married couples who have been married 7 years was asked the number of children they have.The results of the survey are as follows 0 0 0 3 3 3 1 3 2 2 3 1 3 2 4 0 3 3 3 1 0 2 3 3 1 4 2 3 1 3 3 5 0 2 3 0 4 4 2 2 3 2 2 2 2 3 4 3 2 2 1 4 3 2 4 2 1 2 3 2 The data is also in Excel initialize on Blackboard FamilySizeData. xls. (a) Obtain a point estimate for the mean and standard deviation number of children of all couples who have been married 7 years. (b) What is the shape of the distribution of the sample mean? Why? c) Com pute a 95% confidence interval for the mean number of children of all couples who have been married 7 years. Interpret this interval. (d) Compute a 99% confidence interval for the mean number of children of all couples who have been married 7 years. Interpret this interval. (e) You wish to conduct your own study to determine the mean number of children of all couples who have been married 7 years. What sample size would be needed for the estimate to be within 0. 25 (interval length is 0. 5) with 99% confidence if you use the point estimates obtained in part (a)?