TechBuzz is an IT company that monitors the status of large data warehouses. According to TechBuzz, last year the majority of the data servers used by energy-based companies were over-utilized. A sample of 190 servers (all used by energy-based companies) showed that 142 were over-utilized, 12 were used efficiently, and 36 were underutilized. a. What is the point estimate of the proportion of the servers that were under-utilized? b. Determine the margin of error and provide a 95% confidence interval for the proportion of the servers that were over-utilized. c. What is the minimum sample size to ensure that the desired margin of error (in part b) is at most 0.04?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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TechBuzz is an IT company that monitors the status of large data warehouses. According to TechBuzz, last year the majority of the data servers used by energy-based companies were over-utilized. A sample of 190 servers (all used by energy-based companies) showed that 142 were over-utilized, 12 were used efficiently, and 36 were underutilized.

a. What is the point estimate of the proportion of the servers that were under-utilized?
b. Determine the margin of error and provide a 95% confidence interval for the proportion of the servers that were over-utilized.
c. What is the minimum sample size to ensure that the desired margin of error (in
part b) is at most 0.04?

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