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You believe that the mean age of Republican voters is different from the mean age of...

You believe that the mean age of Republican voters is different from the mean age of Democratic voters. To prove your belief, you randomly sample 127 Republican voters and observe a mean age of 52 years with a sample standard deviation of 17 years. From another random sample of 185 Democratic voters, the mean age is 48 years with a sample standard deviation of 21 years. Test your claim at 4% significance. There are 301 degrees of freedom in the appropriate probability distribution.

Math   Statistics-And-Probability   
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Answer #1

Let , be the population mean age of Republican voters and be the population mean age of Democratic voters.

The null and alternative hypothesis is ,

The test is two-tailed test.

Since , df=degrees of freedom=301

The critical values are given by ,

; The Excel function is , =TINV(0.04,301)

The test statistic is ,

Decision : Here , the value of the test does not lies in teh rejection region.

Therefore , fail to reject Ho.

Conclusion : Hence , there is not sufficient evidence to believe that the mean age of Republican voters is different from the mean age of Democratic voters.

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