7. On a factory production line it is important that the time taken to assemble a component is within certain limits. As

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7. On a factory production line it is important that the time
taken to assemble a component is within certain limits. Assembly
times (in minutes) for a single component are recorded for a random
sample of twelve factory workers and the values are as
follows.
11.7 12.8 9.9 10.6 11.6 10.6 13.1 11.2 11.6 11.9 10.9 12.7
a. What is the problem that the management of the factory
concerns?
b. Identify the population of interest in this study.
c. What is the sample currently used?
d. What is the variable of interest in this study? Is the variable
quantitative or qualitative?
e. Calculate the mean and standard deviation of these observed
assembly times.
f. Assuming that the assembly times are normally distributed,
construct a 95% confidence interval for the mean assembly
times.
g. In order to facilitate smooth operation of the entire production
process, the assembly times must satisfy certain conditions. At 5%
significance level, test the hypothesis that the mean assembly time
in the factory is at most 11 minutes.