A Teclear, Inc. call center requires service operators to answer telephone calls from customers in an average time of $0\mathrm{.}15$ minute or less. A sample of $36$ actual operator times was drawn, and the results are given in the following table. In addition, operators are expected to determine customer needs and either respond to them or refer the customer to the proper department within $0\mathrm{.}55$ minute. Another sample of $36$ times was taken for this job com$-$ponent and is also given in the table. If these variables can be considered to be independent, is the average time taken to perform each component sta$-$tistically different from the standard?ComponentMean TimeStandard DeviationAnswer$0\mathrm{.}15230\mathrm{.}0183$Service$0\mathrm{.}5790$A Teclear, Inc. call center requires service operators to answer telephone calls from customers in an average time of $0\mathrm{.}15$ minute or less. A sample of $36$ actual operator times was drawn, and the results are given in the following table. In addition, operators are expected to determine customer needs and either respond to them or refer the customer to the proper department within $0\mathrm{.}55$ minute. Another sample of $36$ times was taken for this job com$-$ponent and is also given in the table. If these variables can be considered to be independent, is the average time taken to perform each component sta$-$tistically different from the standard?ComponentMean TimeStandard DeviationAnswer$0\mathrm{.}15230\mathrm{.}0183$Service$0\mathrm{.}5790$