Question

A regional manager for Wegman’s grocery stores hypothesized average sales for an energy drink are higher when cans of the drink are located on end-of-aisle displays than when the cans are located on middle-aisle displays. To test their hypothesis, the manager compared sales for the energy drink from March 2020 (when the cans were on end-of-aisle displays) to sales for the energy drink from April 2020 (when the cans were on middle-aisle displays) at eight different stores in the Washington, DC, area. The sum of the differences between sales values based on display location equaled 77 cans and the standard deviation of the differences between the sales values equaled 15.5374 cans.

a. What is the calculated value of the associated test statistic?

b. If the level of significance equals 0.05, what is the critical value of the associated test statistic?

c.  Can the manager conclude average sales for an energy drink are higher when cans of the drink are located on end-of-aisle displays than when the cans are located on middle-aisle displays?

Answer 1

SOLUTION:

the given information as follows:

sample size = n = 8

the sum of the difference = $\sum d$ cans

so average difference = $\bar d=\frac{\sum d}{n}=77/8=9.625$

sample standard deviation = 15.5374

the null and alternative hypothesis:

HOM=0

$H_a: \mu_d>0$

= 0,05

since population standard deviation is not knwon so we will use t - distributiion

degree of freedom = n-1 = 8-1 = 7

test statistics:

$t=\frac{\bar d-\mu_d}{S_d/\sqrt{n}}=\frac{9.625-0}{15.5374/\sqrt{8}}=1.752$

critical value of t =

since t = 1.752 < 1.895, so do not reject the null hypothesis

conclusion

it is concluded that there is no evidence to support the manager's claim that the average sales for an energy drink are higher when can of thee drink are located on the end of aisle display than when the can s are located on middle aisle display.

critical value of z