Assume alpha level of 0.05 A survey of voters was seeking to find out if their w

Question

Assume alpha level of 0.05

A survey of voters was seeking to find out if their was any difference between the economic characteristics of Democrats and Republicans. The 58 Democrats in the survey had an average annual income of $53,000 with a standard deviation of about $25, 600. On the other hand, of the 75 Republicans in the survey, the average annual salary was $65,000 with a standard deviation of $29, 200. Test whether or not there is a statistically significant difference between the salaries of Democrats and Republicans.

Explanation / Answer

Hypothesis;

Null hypothesis: x1 - x2 = 0
Alternative hypothesis: x1 - x2 0

Test statistic:

n1 = 58 , x1 = 53000 , s1 = 25600 , n2 = 75 , x2 = 65000 , s2 = 29200

SE = sqrt [(s12/n1) + (s22/n2)]

SE = sqrt [(25600^2/ 58) + (29200^2/ 75)]

= 4761.08

t = [ (x1 - x2) - d ] / SE

= [ (53000 - 65000) - 0 ] / 4761.08

= - 2.52

Now, we need to find p value using t = -2.52 , df = 131

P value =  .012937.

As p value is less than significance level 0 .05

So, we reject the null hypothesis.

There is a statistically significant difference between the salaries of democrats and Republicans

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