a. the average (mean) annual income was less than $50,000

Null and Alternative Hypothesis

H0: mu= 50 (in thousands)

Ha: mu<50 (in thousands)

Level of Significance

Level of Significance = .05

Test Statistic, Critical Value, and Decision Rule

Since alpha = .05, z<-1.645, which is lower tailed

Rejection region is, z<-1.645

Calculate test statistic, x-bar=43.74 and s=14.64

Z=(43.74-50)/2.070=-3.024 2.070 is calculated by: s/sq-root of n

Decision Rule: The calculated test statistic of -3.024 does fall in the rejection region of z<-1.645, therefore I would reject the null and say there is sufficient evidence to indicate mu<50.

Interpretation of Results and Conclusion

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Elements of a Test of Hypothesis

1. Null hypothesis (H0): A theory about the specific values of one or more population parameters. The theory generally represents the status quo, which we adopt until it is proven false. The theory is always stated as H0: parameter = value.

2. Alternative (research) hypothesis (Ha): A theory that contradicts the null hypothesis. The theory generally represents that which we will adopt only when sufficient evidence exists to establish its truth.

3. Test statistic: A sample statistic used to decide whether to reject the null hypothesis.

4. Rejection region: The numerical values of the test statistic for which the null hypothesis will be rejected. The rejection region is chosen so that the probability is α that it will contain the test statistic when the null hypothesis is true, thereby leading to a Type I error. The value of α is usually chosen to be small (e.g., .01, .05, or .10) and is referred to as the level of significance of the test.

5. Assumptions: Clear statement(s) of any assumptions made about the population(s) being sampled.

6. Experiment and calculation of test statistic: Performance of the sampling experiment and determination of the numerical value of the test statistic.

7. Conclusion:

a. If the numerical value of the test statistic falls in the rejection region, we reject the null hypothesis and conclude that the alternative hypothesis is true. We know that the hypothesis-testing process will