Question

Business managers need to know how their decisions will affect the profitability of their businesses. Hypothesis testing allows managers to examine causes and effects before making a crucial management decision. Business managers may use the results of a hypothesis test when making management decisions. Describe how to formulate and test hypothesis about a population mean and/or a population in a business setting. Explain the types of errors that may be possible when conducting a hypothesis test in business application. Explain how business managers can use a hypothesis test in order to explain how much an increase in labor and capital affects productivity. Give examples.

Answer 1

To conduct a hypothesis test of a mean, the following conditions are to be met:

1)The sampling method is simple random sampling.

2)The sampling distribution is normal or nearly normal.

Generally, the sampling distribution will be approximately normally distributed if any of the following conditions apply.

• The population distribution is normal.
• The population distribution is symmetric, unimodal, without outliers, and the sample size is 15 or less.
• The population distribution is moderately skewed, unimodal, without outliers, and the sample size is between 16 and 40.
• The sample size is greater than 40, without outliers.

This approach consists of four steps:

(1) State the hypothesis.

(2) Formulate an analysis plan.

(3) Analyze sample data.

(4) Interpret results.

Types Of Errors that may occur in hypothesis testing:

Type I Errors: False Positives

The first kind of error is the rejection of a true null hypothesis as the result of a test procedure. This kind of error is called a type I error and is sometimes called an error of the first kind.In terms of the courtroom example, a type I error corresponds to convicting an innocent defendant.

Type II Errors: False Negatives

The second kind of error is the failure to reject a false null hypothesis as the result of a test procedure. This sort of error is called a type II error and is also referred to as an error of the second kind.In terms of the courtroom example, a type II error corresponds to acquitting a criminal.

Hypothesis Testing Used in Business to explain increase in labor and capital affects productivity:

Business owners like to know how their decisions will affect their business. Before making decisions, managers may explore the benefits of hypothesis testing, the experimentation of decisions in a "laboratory" setting. By making such tests, managers can have more confidence in their decisions.

Hypothesis testing is discerns the effect of one factor on another by exploring the relationship's statistical significance. For example, one may be interested in how much rainfall affects plant growth. In a business context, a hypothesis test may be set up in order to explain how much an increase in labor affects productivity. Thus, hypothesis testing serves to explore the relationship between two or more variables in an experimental setting. Business managers may then use the results of a hypothesis test when making management decisions. Hypothesis testing allows managers to examine causes and effects before making a crucial management decision.

As hypothesis testing is purely a statistical exercise, data is almost always needed before performing a test. Data may be obtained from economic research agencies or management consultancy firms, who may even carry out the hypothesis testing on behalf of the business. Data are compiled for a given hypothesis. So if a business wishes to explore how economic growth affects a firm's profits, the management consultancy will likely collect data concerning gross domestic product growth and the profit margins of the company over the past 10 or 20 years.

When the management consultancy has collected an adequate amount of data, an equation is set up, which would look something like y=ax+b. Using the same example of economic growth and profits, "x" would denote economic growth while "y" would denote company profits. This is because the company wishes to test the effect of "x" on "y." The parts of the equation the represent real interest is that of "a" and "b." The y-intercept is represented by "b" and the slope of the equation is represented by "a." The hypothesis test focuses on how big "a" is. If "a" were large, then a small change in economic growth would greatly affect company profits. If it were equal to zero, then there would be no effect. The testable hypothesis, or the "null," would be if "a" equals zero. Rejecting the null would imply that economic growth does in fact affect profits.

Hypothesis testing is performed with specialized statistical software that examines the relationship between variables of very large samples. Data are fed into the system and the program does the rest. It is up to the statistician to interpret the results. There are two main variables the statistician is looking for. The first is that of "a" itself. The larger the value of "a," the greater the impact of "x" on "y." The other is that of the critical values. Critical values differ depending on the type of statistical test carried out, but often values represent significance levels of 1, 5 or 10 percent. Rejecting the null at 1 percent implies absolute confidence that "x" has no effect on "y." On the flip side, if the statistician is unable to reject the null even at the 10 percent level, then he could say with a reasonable level that "x" does have an impact on "y," and at a magnitude of "a."

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