# Numerical and Verbal Hypothesis Statement

**Topics:**Statistical inference, Standard deviation, Statistics

**Pages:**3 (680 words)

**Published:**May 25, 2008

In business, small and large or personal the ability to have information to make a decision is essential. “Hypothesis testing is used in both science and business to test assumptions and theories and ultimately guide managers when faced making decisions.” (Doane & Seward, 2007, page 347, Chapter 9). We reviewed and analyzed the data set, Real Estate and developed a hypothesis test. The hypothesis test can be described with the following steps:

Step 1: State the Hypothesis

Does the housing in San Diego cost more than the national average? For this example, we have estimated that average housing cost in San Diego to be $300,000. According to the data set, the national average is $221,103. The null hypothesis is San Diego housing is more than or equal to the national average using a confidence level of 95%. The alternative hypothesis is that San Diego housing is not more than the national average. These two hypotheses are expressed numerically as follows: H0: µ ≥ $ 221.1029

H1: µ < $ 221.1029

Step 2: Specify the Decision Rule

The decision rule is reject the null hypothesis if z > 1.96 or if the p-value is less than alpha. Alpha is this is equal to 0.05. Reject H0 if z > + 1.645

Reject H0 if p < α

Step 3: Calculate the Test statistics:

The above chart represents the national average as proved by the Real Estate data set. The data has been sorted from lowest to highest and divided by six to form the various groups. The descriptive statistics is shown in the table below.

Price

Mean221.1029

Standard Error4.597017

Median213.6

Mode188.3

Standard Deviation47.1054

Sample Variance2218.919

Kurtosis-0.2768

Skewness0.474013

Range220.3

Minimum125

Maximum345.3

Sum23215.8

Count105

Using the numbers from the table, the z value for San Diego is calculated as follows: x̄ = 300,000 z = x̄- μ/s√n,

μ = 221.1029 z =...

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