Question

In Exercises 1–5, use the following survey results: Randomly selected subjects were asked if they were aware that the Earth has lost half of its wildlife population during the past 50 years. Among 1121 women, 23% said that they were aware. Among 1084 men, 26% said that they were aware (based on data from a Harris poll).

Biodiversity: Identify the null and alternative hypotheses resulting from the claim that for the people who were aware of the statement, the proportion of women is equal to the proportion of men.

Short answer

Null hypothesis: The proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

\({H_0}:{p_1} = {p_2}\)

Alternate Hypothesis: The proportion of women who were about the factthat the Earth has lost half of its wildlife population during the past 50 years is not equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

\({H_1}:{p_1} \ne {\rm{ }}{p_2}\)

Step-by-step solution

Given information

In a sample of 1121 women, 23% said that they were aware of the fact that the Earth has lost half of its wildlife population during the past 50 years. In another sample of 1084 men, 26% said that they were aware that the Earth has lost half of its wildlife population during the past 50 years.

Describe the hypotheses

It is claimed that the proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

The following hypotheses are set up:

Null hypothesis:The proportion of women who were about the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware of the fact that the Earth has lost half of its wildlife population during the past 50 years.

Symbolically,

\({H_0}:{p_1} = {p_2}\)

Alternate Hypothesis:The proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years was not equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

Symbolically,

\({H_1}:{p_1} \ne {\rm{ }}{p_2}\)