In: Statistics and Probability
Hypotheses are defined as:
The null hypothesis represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument but has not been proved. The null hypothesis offers close to null prediction.
The hypothesis actually to be tested is usually given the symbol H0 and is commonly referred to as the null hypothesis. The null hypothesis is assumed to be true unless there is strong evidence to the contrary —similar to how a person is assumed to be innocent until proven guilty.
The alternative hypothesis is a statement of what a hypothesis test is set up to establish. The other hypothesis, which is assumed to be true when the null hypothesis is false, is referred to as the alternative hypothesis and is often symbolized by HA or H1.
For this assignment, select two different business research scenarios you are interested in testing.
Write a set of hypotheses for each scenario.
In Business scenario Hypothesis testing plays a major in deciding a company’s marketing strategy. Below are few business scenarios where we can use hypothesis testing for devising strategy:
(1) A company is getting less turnover from their sales. They are willing to going to increase its advertisement. But before they do so they are willing to check from Historical (previous year’s) data that whether the increase advertisement increases the sales of the company or not. Based on the study they’ll be devising a strategy whether to increase advertisement or not.
So, for this purpose Hypotheses can be considered as:
H0: Increase in advertisement doesn’t affect the sales of the company.
v/s
H1: Increase in advertisement increases the sales of the company.
Or mathematically we can check the Regression Equation between the two variables Y(sales) and X(advertisement) and can conclude based on the significance of the Model. (p-value)
Term |
Coef |
SE Coef |
T-Value |
P-Value |
VIF |
Constant |
5.58 |
3.72 |
1.50 |
0.185 |
|
Advertisement Budget(millions) |
1.805 |
0.146 |
12.35 |
0.000 |
1.00 |
From the p-value (0.000) <0.005 we can conclude that the advertisement have significant effect on sales. (since the null hypothesis is rejected)
Regression Equation
Sales(millions) = 5.58 + 1.805 Advertisement Budget (millions)
(2) An International Newspaper company wants to know if changing their headlines to Spanish will increase the number of reads. For this purpose we will perform a paired t-test before and after the change to conclude on the fact based on the p-value as above.
The Hypothesis considered here is:
H0: Changing an English headline into a Spanish headline will have no effect on clickthrough rate (quantifying the number of reads)
v/s
H1: Changing an English headline into a Spanish headline will increase clickthrough rate
Or mathematically,
H0: µbefore = µafter v/s H1: µbefore ≠ µafter