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 Assume that a P-value of 0.1 is obtained when testing the claim given in Exercise 1 “Biodiversity.” What should be concluded about the null hypothesis? What should be the final conclusion?

Short answer

The null hypothesis fails to be rejected.

There is insufficient evidence to reject the claim that the proportion of women who were aware of the fact is equal to the proportion of men who were aware of the fact.

Step-by-step solution

Step 1: 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 1048 men, 26% said that they were aware that the Earth has lost half of its wildlife population during the past 50 years.

It is claimed that the proportion of women who were about the fact is equal to the proportion of men who were aware of the fact.

Formulation of the hypotheses

Null hypothesis: The proportion of women who were aware of the factis equal to the proportion of men who were aware of the fact.

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

Alternative hypothesis:The proportion of women who were aware of the factis not equal to the proportion of men who were aware of the fact.

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

Interpretation of the p-value

The p-value is equal to 0.1.

Let the level of significance be equal to 0.05.

Since the p-value is greater than 0.05, the null hypothesis fails to be rejected.

There is insufficient evidence to reject the claimthat the proportion of women who were aware of the factis equal to the proportion of men who were aware of the fact.