Question

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 2222 stores this year shows mean sales of 6868 units of a small appliance, with a standard deviation of 66 units. During the same point in time last year, an SRS of 2323 stores had mean sales of 62.962.9 units, with standard deviation 15.715.7 units. An increase from 62.962.9 to 6868 is a rise of about 8%.

1. Construct a 99% confidence interval estimate of the difference μ1−μ2μ1−μ2, where μ1μ1 is the mean of this year's sales and μ2μ2 is the mean of last year's sales.

(a)  <(μ1−μ2)<<(μ1−μ2)<

(b) The margin of error is  .

2. At a 0.010.01 significance level, is there sufficient evidence to show that sales this year are different from last year?

A. Yes
B. No

Answer 1

Answer 1

(A) Using TI 84 calculator

press stat then tests then 2-sampTInt

x1 = 68

s1 = 6

n1 = 22

x2 = 62.9

s2 = 15.7

n2 = 23

c-level = 0.99

Pooled: No

press ENTER, we get

(B) Margin of error = (upper limit - lower limit)/2

= (15.0502 - (-4.8502))/2

= 9.9502

Answer 2

No, at 0.01 significance level we have insufficient evidence to conclude that the sales this year are different from last year because the 99% confidence interval includes 0 values.

So, answer is NO