due 나15 1 mean confidence intervals and hypothesis test practice On your own piece of paper, work all four problems completely. Please note problem 1 does not require the 4-part process to be completed. It is a question that practices the conceptual relationships we have been discussing. It has been found that a certain machine that fills "5-pound" sacks of sugar actually fills the sacks with an amount that varies from sack to sack according to a normal distribution. Suppose that a 99% confidence interval has been calculated for the mean of the population of all sacks filled by this process. 1. (a) Would the width (or margin of error) of your confidence interval increase or decrease if the management decides to increase the sample size used? Explain why. Would the width (or margin of error) of your confidence interval increase or decrease if the process is improved so that the standard deviation drops ? Explain why. (b) Would the width (or margin of error) of your confidence interval increase or decrease if a 95% rather than 99% confidence interval is chosen? Explain why. (c) The Roman Arches is an Italian restaurant. The Manager wants to estimate the average amount a customer spends on lunch Monday through Friday. A random sample of 115 customers' lunch tabs gave a mean of $9.74 with a standard deviation of $2.93. Construct and interpret a 90% confidence interval for the average amount spent on lunch by all 2. customers. 3. Cholesterol level in a particular male population is assumed to follow a normal distribution. A random sample of size 16 has a sample mean of 245 and a standard deviation of 32 units. Construct and interpret a 95% confidence interval for the mean cholesterol level in the population. A school reports that the mean number of hours their students study each week is 15 hours. The students believe the mean is not 15 hours. To test their claim, they select a random sample of 49 students and find the sample mean is 16.163 hours with a sample standard deviation of 4.41 hours. Is there any evidence to support their belief at a 0.05 level of significance? 4.

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