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University of California, Irvine - STATS 67Homework5+Solution

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University of California at Irvine Department of Statistics Statistics 67 Winter Quarter 2016 Homework 5. SOLUTION. 1. (10 points) In order to ensure efficient usage of a server, it is necessary to estimate the mean ...

University of California at Irvine Department of Statistics Statistics 67 Winter Quarter 2016 Homework 5. SOLUTION. 1. (10 points) In order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users. According to records, the average number of concurrent users at 100 randomly selected times is 37.7, with a standard deviation σ = 9:2 (a) (5 points) Construct a 90% confidence interval for the expectation of the number of concurrent users. (b) (5 points) At the 1% significance level, do these data provide significant evidence that the mean number of concurrent users is greater than 35? Answer: 2. (10 points) Installation of a certain hardware takes random time with a standard deviation of 5 minutes. (a) (5 points) A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 95% confidence interval for the population mean installation time. (b) (5 points) Suppose that the population mean installation time is 40 minutes. A technician installs the hardware on your PC. What is the probability that the installation time will be within the interval computed in (a)? Answer: 3. (25 points) A survey asked students their heights and whether they preferred to sit in the front, middle, or back of the class. The following data are the heights of the 15 females in the sample who said they prefer to sit in the back. 68, 62, 65, 69, 68, 69, 64, 66, 69, 68, 62, 64, 67, 68, 65 The mean height for the population of college females is 65 inches. Does this sample provide a significant evidence that females who prefer to sit in the back of the room are taller than average? Use a α = 0:05. (a) (5 points) What is the sample mean height X¯? (b) (5 points) What are the null and alternative hypotheses being tested? Write them in symbols and define your symbols. (c) (5 points) What is the null standard error ? (d) (5 points) Compute the values of test statistics and test p{value. (e) (5 points) What conclusion would be made in this situation? Answer:

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