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The proportion of people with blue eyes is equal to 0.35.

Let p be the population proportion of people with blue eyes.

According to the stated claim, the following hypotheses are set up:

Null hypothesis \({H_0}:p = 0.35\).

Alternative hypothesis \({H_A}:p \ne 0.35\).

The two types of errors made while conducting hypotheses tests are defined below.

Type I error: Rejecting the null hypothesis when the null hypothesis is true is a type I error and is denoted by\(\alpha \).

Type II error: Failing to reject the null hypothesis when the null hypothesis is false is a type II error and is denoted by\(\beta \).

In accordance with the given claim, the following statements define the type I error and the type II error:

Type I error: When the actual value of the proportion is equal to 0.35, and the researcher rejects the claim \(p = 0.35\), a type I error is made.

Type II error: When the actual value of the proportion is not equal to 0.35, and the researcher fails to reject the claim \(p = 0.35\), a type II error is made.