MATH 1342 Core Assessment : Describe and compute confidence intervals. Question #1: Describe and compute confidence intervals. Bob was given the following problem: A survey of 30 emergency room patients found that the average waiting time for treatment was 174.3 minutes. Assuming that the sample standard deviation is 46.5 minutes, construct a 99% confidence interval to find the population mean wait time. Bob’s work is shown below to construct the 99% confidence interval. Find his mistake and briefly explain what must be done to correct his solution. 46.5 46.5 174.3 − 2.575 174.3 + 2.575 30 30 174.3 − 21.9 174.3 + 21.9 152.4 196.2 I am 99% confident that the mean wait time for emergency room treatment is between 152.4 and 196.2 minutes. a) Using complete sentences, describe the mistake and briefly explain what Bob must do to correct his solution. Hint: should Bob use z-distribution or t-distribution test ? The sample size is less than 30. How to fix it? b) Using the correct method you found in Part A, construct the actual 99% confident interval. Hint : provide the confident interval c) ( ___ < μ < ___) Using complete sentences, interpret the new confidence interval found in Part B. Hint: _______ % confident that the mean wait time for emergency room treatment is between __________ and __________ minutes. Question #2 Describe and compute confidence intervals. A company wants to decide how to label their bags of dog food (in pounds). The filling machine inevitably experiences fluctuations in filling, so a quality control manager randomly samples 12 bags of dog food from the storage facility and measures their contents. She obtains the following data: 15.94 15.74 16.24 15.36 15.84 15.84 15.52 16.16 15.78 15.51 16.28 16.53 a) Confirm that there are no outliers by constructing a boxplot. Hint: Use Boxplot in section 2.5 to define if any outlier b) Determine the sample mean and the sample standard deviation. Hint: use TI-83/84 to compute sample mean and sample standard deviation c) Show work to construct a 90% confidence interval for the population variance. Hint : provide the confident interval ( __< σ < __) d) Using complete sentences, interpret this interval. (Hint: ____% confident that the population variance of the amount of dog food is between ________ and __________ pounds.

**Describe and compute confidence intervals. Question #1: Describe and compute confidence intervals.**

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