2. A study is done to determine if Company A retains its workers longer than Company B. It is believed that Company A has a higher retention than Company B. The study finds that in a sample of 11 workers at Company A their average time with the company is four years with a population standard deviation of 1.5 years. A sample of 9 workers at Company B finds that the average time with the company was 3.5 years with a population standard deviation of 1 year. Test this proposition at the $$ 1 \% $$ level of significance. Use critical value approach.

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The test statistic is 0.8899, and the critical value is 2.552. Failing to reject the null hypothesis, we do not have enough evidence to conclude that Company A retains its workers longer than Company B at the $$1\%$$ level of significance.

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