Question

Finer Diner Average Table Hypothesis
Explain the process you used to test the hypothesis and what value would sigma have to be in order for the decision to be reversed?

Answer 1

Definition: -

The Hypothesis Testing is a statistical test used to determine whether the hypothesis assumed for the sample of data stands true for the entire population or not. Simply, the hypothesis is an assumption which is tested to determine the relationship between two data sets.

In hypothesis testing, two opposing hypotheses about a population are formed Viz. Null Hypothesis (H0) and Alternative Hypothesis (H1). The Null hypothesis is the statement which asserts that there is no difference between the sample statistic and population parameter and is the one which is tested, while the alternative hypothesis is the statement which stands true if the null hypothesis is rejected.

The following Hypothesis Testing Procedure is followed to test the assumption made.:

Set up a Hypothesis

Set up a suitable Significance Level

Determining a suitable Test Statistic

Determining the Critical Region

Performing computations

Decision-making

While testing the hypothesis, an individual may commit the following types of error:

Type-I Error: -

True Null hypothesis is rejected, i.e. hypothesis is rejected when it should be accepted. The probability of committing the type-I error is denoted by α and is called as a level of significance.

If, α = Pr[type-I error] = Pr [reject H0/H0 is true]

Then, (1-α) = Pr[accept H0/H0 is true]

(1-α) = corresponds to the concept of Confidence Interval.

Type-II Error: -

A False Null hypothesis is accepted, i.e. hypothesis is accepted when it should be rejected. The probability of committing the type-II error is denoted by β.

If, β = Pr[type-II error] = Pr[accept H0/H0 is false]

Then, (1-β) = Pr[reject Ho/H0 is false

(1-β) = power of a statistical test.

Decision is: The Null Hypothesis is True False (1-a) Confidence Level Accept Ho Reject Ho (1-B) Power of the test

The Z test formula is given as: = Z σ Vn Where, is the sample mean u is the population mean a is the standard deviation and n is the sample size.

Thus, hypothesis testing is the important method in the statistical inference that measures the deviations in the sample data from the population parameter. The hypothesis tests are widely used in the business and industry for making the crucial business decisions