The records of the 100 postal employees show that the average time these employees have worked for the postal service is 𝑥𝑥 = 9 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦. Assume we know that the time the population of U.S. postal service employees have spent with the postal service is approximately Normal, with standard deviation 𝜎𝜎 = 5 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦.
a. (2 points) Which value is a parameter, and which value is a statistic?
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b. (2 points) Calculate a 95% confidence interval for the mean time 𝜇𝜇 the population of U.S. postal service employees have spent with the postal service. Show your work. Round to the nearest 0.1 year and report your answer as (*,*).
c. (2 points) Interpret the 95% confidence interval in the context of this data.
d. (4 points) You learn the records solely came from a postal station in a large city, and that we do not know how the 100 records were obtained. Based on the data collection method, you determine the 95% confidence interval for the mean time 𝜇𝜇 the population of U.S. postal service employees is not reliable.
(i) (2 points) What three conditions are needed to estimate a confidence interval?
(ii) (2 points) Identify two reasons why the confidence interval is not trustworthy.