# Hypothesis Testing & Confidence Interval: Wages

Assume that the average national wage for all educational levels is $15 with a standard deviation of $4. We want to find out whether individuals with higher education tend to make higher wages than on the average nationally for all educational levels. Our null hypothesis is that individuals with an educational level higher than high school do not make higher wages than the average wage for all Americans with any educational level. Our alternative hypothesis is that individuals with an education higher than high school do make higher wages than the wage of an average American. On a new tab in the Excel spreadsheet, list the wages for all observations in which education was higher than 12 (higher than a high school degree). Calculate the mean and the standard error of the mean for wages for this sample. Your standard error of the mean should use the unbiased standard deviation (you can use either the population standard deviation, which is by nature unbiased, or you can calculate the unbiased standard deviation of the sample using formula 2.5).

1.) Calculate the Z score for the wage sample you constructed in #2 comparing the sample means to the national mean ("z score for groups").

2.)Find the probability that a random sample of persons in the U.S. could have a mean of wages as high as the mean of the wages in your sample of higher educated individuals (use the Z score from #3 to find the area beyond Z).

3.)Is the null hypothesis rejected at a 0.05 significance level?

4.)Calculate a 95% confidence interval CI for the mean wage for your sample using an unbiased standard deviation.

5.)Interpret the CI

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Probability, Sampling Distribution, and Tools of Inference

Assume that the average national wage for all educational levels is $15 with a standard deviation of $4. We want to find out whether individuals with higher education tend to make higher wages than on the average nationally for all educational levels. Our null hypothesis is that individuals with an educational level higher than high school do not make higher wages than the average wage for all Americans with any educational level. Our alternative hypothesis is that individuals with an education higher than high school do make higher wages than the wage of an average American. On a new tab in the Excel spreadsheet, list the wages for all observations in which education was higher than 12 (higher than a high school degree). ...

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis and confidence interval. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.