<p> IENG 492</p><p>Hwk 1</p><p>1. A sample of 20 cigarettes is tested to determine nicotine content and the average value observed was 1.2 mg. Compute a 99 percent two-sided confidence interval for the mean nicotine content of a cigarette if it is known that the standard deviation of a cigarette’s nicotine content is σ = 0.2 mg.</p><p>2. In Problem 1, suppose that the population variance is not known in advance of the experiment. If the sample variance is 0.04, compute a 99% two-sided confidence interval for the mean nicotine content.</p><p>3. The daily dissolved oxygen concentration for a water stream has been recorded over 30 days. If the sample average of the 30 values is 2.5 mg/liter and the sample standard deviation is 2.12 mg/liter, determine a value which, with 90 percent confidence, exceeds the mean daily concentration.</p><p>4. Suppose that when sampling from a normal population having an unknown mean µ and unknown variance σ2, we wish to determine a sample size n so as to guarantee that the resulting 100(1 – α) percent confidence interval for µ will be of size no greater than A, for given values α and A. Explain how we can approximately do this by a double sampling scheme that first takes a subsample of size 30 and then chooses the total sample size by using the results of the first subsample.</p>