1. A study conducted in March 2009 found that about half of U.S. adults trusted the...

1. A study conducted in March 2009 found that about half of U.S. adults trusted the U.S. government more than U.S. business to solve the economic problems of the United States. However, when the population is subdivided by political party affiliation, the results are very different. The study showed that 72% of Democrats trusted the government more, but only 29% of Republicans trusted the government more. Suppose that you are in charge of updating the study. You will take a national sample of Democrats and a national sample of Republicans and then try to use the results to show statistical evidence that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more tan business.

a. What are the null and alternative hypotheses? b.

What is a Type I error in the context of this study?

c. What is a Type II error in the context of this study?

Solutions

Expert Solution

a. The hypothesis is,

Null hypothesis is that the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business.

Alternate Hypothesis is that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more than business.

Type I error occurs when we reject the true null hypothesis.

If we reject that the the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business. When in fact they are equal, then we commit type I error.

Type II occurs when we fail to reject the false null hypothesis.

If we fail to reject that the the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business. When in fact they are unequal(i.e., the proportion of Democrats is greater than the proportion of Republicans, then we commit type II error.

orchestra answered 1 year ago

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