Sample Hypothesis Test: Select The Variables

Sample Hypothesis Test
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Sample Hypothesis Test
The two-sample test is commonly used for hypothesis tests; it is used to compare two variables to understand whether the average difference between the two groups is significant. Conducting a two-sample hypothesis test requires four steps that are to state the hypothesis, formulating an analysis plan, analyzing data and interpreting results. In a two-sample hypothesis test, two parameters are generated from two different populations (Pfister & Janczyk, 2013).
For a two sample hypothesis test the null hypothesis Ho usually state that there is no difference between the two parameters of the two variables the null hypothesis is symbolized by , =, or . The alternative hypothesis Ha is a statistical hypothesis that determines if the claim is true. The alternative hypothesis is represented by the symbol >, or <. There are specific conditions that are important when performing a two-sample test between two populations is symbolized by μ1 and μ2 (Hothorn & Everitt, 2014).
The sample needs to be randomly selected and can be independent meaning that the sample selected from one population should be different from the sample of the second population or dependent whereby the sample related. Performing a two-sample test, the standardized test statistic is
(Kass, Eden & Brown, 2014).
In situations where the variances are the same the data from the two samples is put together to estimate the standard deviation which is symbolized by as shown below
(Kass, Eden & Brown, 2014).
In this case, the standard error for sampling distribution is calculated as follows when variances are equal
(Kass, Eden & Brown, 2014).
Example
In a random sample whereby 17 police officers have a mean yearly income of $ 35,800 with the standard deviation of $ 7,800. In the nearby town, a random sample of 18 police officers shows a mean of $ 35, 1000 annually and a standard deviation of $ 7,375. To conduct a two sample test to test this claim at = 0.01 whereby the yearly income for the two towns are not the same assuming that the population variances are the same the following is the steps
H0: U2 = U2
H0: U1 = U2
Claim = Ha: U1 = U2
d.f = n1 + n2 – 2
= 17 + 18 -2 = 33
The standardized test statistic is
= 0.273
The results indicate that there is insufficient evidence to claim that the mean of ann...