Business Statistics: Hypothesis Testing
Define
The probability distribution of all the possible values a sample statistic can take is called the sampling distribution. of the statistic. The keyword here is “sample statistic”.
The sample mean and sample proportion based on a random sample are examples of sample statistics.
Concept of Standard Error
What is the standard deviation of the sample statistic called? Can you guess? It is called the Standard Error of the Statistic.
The standard deviation of the distribution of the sample means is called the standard error of the mean. Likewise, the standard deviation of the distribution of the sample proportions is called the standard error of the proportion.
Image:https://www.wikihow.com/Calculate-Mean,-Standard-Deviation,-and-Standard-Error
Central Limit Theorem
The distinguishing and unique feature of the central limit theorem is that irrespective of the shape of the distribution of the original population, the sampling distribution of the mean will approach a normal distribution as the size of the sample increases and becomes large.
Statistical Hypothesis
A statistical hypothesis is a statement about a population parameter. It may or may not be true. The manager has to ascertain the truth of the hypothesis.
Null and Alternative Hypothesis
A Null Hypothesis is the status quo. It is so formulated that its rejection leads to the desired conclusion which is the Alternative Hypothesis. Researchers and Decision Makers generally want to prove the Alternative Hypothesis.
ImageCredites:https://www.majordifferences.com/2016/10/5-differences-between-null-and.html#.YKQjB6gza00
Type I and Type II Error
Hypothesis Testing –Marketing Example
Kuldeep, product manager for a line of apparel, to introduce the product line into a new market area
A Survey of a random sample of 400 households in that market showed a mean income per household of $30,000. The standard deviation of the population based on a pilot study is $8,000.
Kuldeep strongly believes the product line will be adequately profitable only in markets where the mean household income is greater than $29,000.
Should Kuldeep introduce the product line into the new market?
To reach a final decision, Kuldeep has to make a general inference (about the population) from the sample data
Criterion — mean income across all households in the market area under consideration
If the mean population household income is greater than $29,000, Kuldeep should introduce the product line into the new market.
Kuldeep’s Hypothesis
Kuldeep’s decision-making is equivalent to either accepting or rejecting the hypothesis: The population means household income in the new market area is greater than $29,000.
One-Tailed Hypothesis Test
The term one-tailed signifies that all — or z-values that would cause Karen to reject H0, are in just one tail of the sampling distribution
- m = Population Mean
- H0: m >= $29,000
- Ha: m > $29,000
Test Statistic
Substituting the values in the formula given below for the unknown terms, we get Z =2.5.
Since the computed Z value falls in the rejection region, reject the null hypothesis and introduce the product line into the new market area.
Critical Value for Rejecting the Null Hypothesis
P-Value — Actual Significance Level
The probability of obtaining a Z value that is greater than Z computed (and in this case Z computed is 2.5) = .0062.
This value is sometimes called the actual significance level, or the p-value. This is the level at which the null hypothesis gets rejected. The actual significance level of .0062, in this case, means the odds are less than 62 out of 10,000 that the sample means income of $30,000 would have occurred entirely due to chance (when the population means income is $29,000 or less). Since P-Value is less than alpha the level of significance(5%), the null hypothesis is rejected. The decision is to introduce the product line into the new market area.
Hope you really enjoyed the pictorial view of the Hypothesis. Keep learning..!
