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 14 stores this year shows mean sales of 79 units of a small appliance, with a standard deviation of 10 units. During the same point in time last year, an SRS of 12 stores had mean sales of 88.7 units, with standard deviation 10.2 units. A decrease from 88.7 to 79 is a drop of about 12%. 1. Construct a 95% confidence interval estimate of the difference ?1??2, where ?1 is the mean of this year's sales and ?2 is the mean of last year's sales. (a) <(?1??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. Yes B. No

Answer 1

Answer 1

(A) using TI 84 calculator

press stat then tests then 2-sampTInt

enter the data

x1 =79

s1 = 10

n1 = 14

x2 = 88.7

s2 = 10.2

n2 = 12

c-level = 0.95

Pooled: No

press enter, we get

(b) margin of error = (upper limit - lower limit)/2

= (-1.48-(-17.92))/2

= 16.44/2

= 8.22

Answer 2

yes, there is sufficient evidence  to show that sales this year are different from last year because the confidence interval does not include 0, which means that the difference is significantly different from 0

YES