Chapter 7, Problem 1UA

EXERCISES

In Exercises 1–3, assume that you work for the Internal Revenue Service. You are asked to write a report about the claim that 57% of U.S. adults think the amount of federal income tax they pay is too high. (Source: Gallup)

1. 1. What is the null hypothesis in this situation? Describe how your report could be incorrect by trying to prove the null hypothesis.
2. 2. Describe how your report could make a type I error.
3. 3. Describe how your report could make a type II error.

To determine

To state: The null hypothesis in the given situation and describe how the report could be incorrect by trying to prove the null hypothesis.

Answer to Problem 1UA

The null hypothesis in the given situation is, $H_0:p=0.57$.

When type error is present, the report could be incorrect by trying to prove the null hypothesis.

Explanation of Solution

Null hypothesis:

Null hypothesis is a statement about the population parameter. Its value is equal to the claim value, which is denoted by $H_0$. The population parameter can be the mean, standard deviation, proportion, variance, and so forth. The possible symbols used in the null hypothesis would be $\le ,\ge$ or $=$.

Alternative hypothesis:

It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by $H_1$.

Here, the claim is that, “57% of U.S adults think the amount of federal income tax they pay is too high”. This can be written as $p=0.57$. The complement of the claim is $p\ne 0.57$.

Null hypothesis: $H_0:p=0.57$

Type I error: Rejecting the null hypothesis, when it is actually true.

Type II error: Failing to reject the null hypothesis, when it is false.

A type I error occurs when the hypothesis test indicates that the percentage of U.S. adults think the amount of federal income tax they pay is too high is not 57%; but in reality, the percentage of U.S. adults think the amount of federal income tax they pay is too high is 57%. Thus, the report could be incorrect by trying to prove the null hypothesis when the type error I is present.