A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of $14$ stores this year shows mean sales of $70$ units of a small appliance, with a standard deviation of $6.8$ units. During the same point in time last year, an SRS of $27$ stores had mean sales of $63.132$ units, with standard deviation $6.3$ units. An increase from $63.132$ to $70$ is a rise of about 10%.

1. Construct a 95% confidence interval estimate of the difference $\mu_1 - \mu_2$, where $\mu_1$ is the mean of this year's sales and $\mu_2$ is the mean of last year's sales.

(a) $< (\mu_1 - \mu_2) <$

(b) The margin of error is .

2. At a $0.05$ significance level, is there sufficient evidence to show that sales this year are different from last year?

A. No
B. Yes