A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods.
The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):

Before visit: 57.1 94.6 49.2 77.4 43.2
After visit: 63.5 101.8 57.8 81.2 41.9

Do the data indicate that the average net sales improved? (Use a= 0.05)

We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved

Step-by-step explanation:

Let put some notation  

x=test value before , y = test value after

x: 57.1 94.6 49.2 77.4 43.2

y: 63.5 101.8 57.8 81.2 41.9

The system of hypothesis for this case are:

Null hypothesis:

Alternative hypothesis:

The first step is calculate the difference and we obtain this:

d: 6.4, 7.2, 8.6, 3.8, -1.3

The second step is calculate the mean difference  

The third step would be calculate the standard deviation for the differences, and we got:

The next step is calculate the statistic given by :

The next step is calculate the degrees of freedom given by:

Now we can calculate the p value, since we have a right tailed test the p value is given by:

We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1