Inferential Statistics

# hypothesis test for difference between means

In this case, as in the mean case, it all begins with an “a priori” assumption that the value of both means is equal, μ_{1} = μ_{2}. Then we use

which are calculated by obtaining a random sample from both populations in order to decide if the assumption that μ_{1} = μ_{2} is likely. We will follow these steps:

Example: We studied two samples (A and B) of Andalusian citizens of 80 members each, to know about their nationalistic sentiment. On a scale of 1 to 10, the first group averaged 7.2 with standard deviation of 3.1, while the second group averaged 8.1 with a standard deviation of 4.2. Our research hypothesis is that group B has a greater nationalist sentiment than collective A. Check the hypothesis for a significance level of 0.01.

Step 1: H

_{0}: μ_{1}≥ μ_{2}; H_{1}: μ_{1}< μ_{2}Step 2: This is a one-tailed test with α = 0.01, then the critical value z

_{α}= -2.33Step 3: n is great enough, so we can apply the distribution N(0, 1)

Step 4:

We reject the alternative hypothesis; therefore, there are no significant differences between the level of nationalist sentiment for both groups

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