Answer to Question #253662 in Statistics and Probability for Goldie

Question

a. State the hypotheses and identify the claim.

b. Find the critical value(s)

c. Find the test value

d. Make the decision

e. Summarize the result

The manager of the cosmetics section of a large department store wants to determine whether newspaper advertising really does affect sales. For her experiment, she randomly selects 15 items currently in stock and proceeds to establish a baseline. The 15 items are priced at their usual competitive values, and the quantity of each item sold for a 1-week period is recorded. Then, without changing their price, she places a large ad in the newspaper, advertising the 15 items. Again, she records the quantity sold for a 1-week period. The results follow. 

Item : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

No. of Items Sold Before Ad: 25 18 3 42 16 20 23 32 60 40 27 7 13 23 16

No. of Items Sold After Ad  : 32 24 7 40 19 25 23 35 60 43 28 11 12 32 28

Using ∝= 0.05, two-tailed test. Analyze the data then interpret the result.

Answer 1

$H_0:\mu_1= \mu_2$

$H_a:\mu_1\neq \mu_2$

where $\mu_1$ is mean No. of Items Sold Before Ad,

$\mu_2$ is mean No. of Items Sold After Ad.

null hypothesis: newspaper advertising does not affect sales

alternative hypothesis: newspaper advertising really does affect sales

$\mu_1=24.33,\sigma_1=14.59$

$\mu_2=27.93,\sigma_2=13.60$

$t=\frac{\mu_2-\mu_1}{\sqrt{(\sigma_1^2+\sigma_2^2)/n}}=0.699$

$df=\frac{(n-1)(\sigma_1^2+\sigma_2^2)^2}{\sigma_1^4+\sigma_2^4}=27.86$

critical value:

$t_{crit}=2.048$

Since $t<t_{crit}$ , we can accept the null hypothesis: newspaper advertising does not affect sales.