Question

use any data and answers those questions There are several stores that or businesses that set these types of goals. Would this tell us an overall average? For example lets just say the sales goal is 100,000 a month, this month 98,000 is sold that is clearly less than the goal. However is that what the test tells us? Or does it look at a long term average over several months? Why is it valuable to know if the results are statistically signficant?

thank you

Did Sales Reach Target Value?

            Business requires careful planning because storing goods is associated with the additional costs. Thus, business sets monthly revenue goals, and understanding if the sales have reached the monthly revenue goal is important. Let us take a retail chain, and suppose they have monthly revenues of the stores, and a certain goal revenue.

            In this case, the four-step hypothesis testing is as follows:

1) The null hypothesis suggests that the mean stores sale does not significantly differ from the goal value. The alternate hypothesis is opposite to null and it suggests that the difference between the mean stores sales and goal value is significantly different (Triola, 2015).

2) The decision rule is set according to the significance level. For this case, we can set the significance level 0.1 because we do not require the highest precision. Thus, if the significance of the calculated t-value exceeds 0.1, we do not have enough evidence to reject the null hypothesis. Otherwise, we reject the null and accept the alternate hypothesis (Ott, Longnecker & Draper, 2016).

3) At this stage, we calculate the test statistics using mean value, goal revenue, standard deviation of the mean (s), and the number of observations (n):

                           t=(Mean-Goal)/s/square root of n

.

Also, we obtain the significance of this t-value from statistical tables or statistical software. Afterwards, we compare the value with the significance level (Triola, 2015).

            4) The final step is interpretation of the statistical test for the real life situation. If the test confirms the null hypothesis, this means that the mean stores sales are approximately equal to the goal value. If the null is rejected, then the store chain underperforms, which is an important information for the management (Black, 2017).

            Therefore, in this problem t-test was used as a support for the decision-making process in management. It provides a statistical background for sales analysis of the store chain and provides management with the valuable information about business (Black, 2017).

  There are several stores that or businesses that set these types of goals. Would this tell us an overall average? For example lets just say the sales goal is 100,000 a month, this month 98,000 is sold that is clearly less than the goal. However is that what the test tells us? Or does it look at a long term average over several months? Why is it valuable to know if the results are statistically signficant?

Answer 1

We will assume data for one of similar stores whose goal of revenue is 100 per month. Following is the data which we have generated from a simple normal function with mean of 100 and standard deviation 2. Data is for 24 months:

97.32556 99.08293 96.36508 102.03099 100.76817 98.45980 100.29330 101.70138 103.32016
102.41942 101.32686 100.76731 105.57869 101.12053 100.43613 98.03960 98.99415 97.90191
98.99785 99.88415 102.74205 99.72105 98.89522 100.58489

Now, we can see that our goal was 100 but in many of the months it is less than 100, does that mean that store did not reach the target? The answer to this question is NO, we cannot just say like that, because it might have happened due to natural variation.

So, the idea is when we check for our average revenue goal we check for a long term average and not individual monthly revenue.

But how to tell that whether the store is doing good to meet the goal or not, for that we will do a t-test to check if there is a statistically significant difference i.e. the variation is not due to natural variation but indeed the store is not performing well enough to meet its target revenue. For doing a t-test we will have to select a significance level which is .1.

Now, We will calculate the t-statistic for our sample using R:

One Sample t-test

One Sample t-test

data: ac_1
t = 0.95119, df = 23, p-value = 0.3514
alternative hypothesis: true mean is not equal to 100
90 percent confidence interval:
99.59161 101.42703
sample estimates:
mean of x
100.5093

Let us understand the results of t-test. The t-value here is 0.95119, degree of freedom is 23 which is equal to number of observations -1, here we had 24 observation. The p-value is 0.3514 which is greater than 0.1 (our significance level), Thus we cannot reject the null-hypothesis that indeed on an average the store is generating the target revenue of 100.

Another way to check for null hypothesis is by looking at the confidence interval which is [99.59161,101.42703] which contains 100, thus we cannot reject the null hypothesis at 90% confidence level.

Thus from our test we cannot say that the store is not meeting its revenue goal at an average, thus in months where revenue is less happened due to normal variation.