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 When testing the claim that\({p_1} = {p_2}\), a test statistic of z = -1.64 is obtained. Find the P-value for the hypothesis test.

Short answer

The p-value is equal to 0.1010.

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 had lost half of its wildlife population during the past 50 years. It is claimed that the two population proportions are equal.

Find the p-value

The given claim has an equality sign. This implies that the alternative hypothesis for testing the claim will be as follows:

Alternate Hypothesis: The proportion of women who were aware of the fact is not equal tothe proportion of men who were aware of the given fact.

Symbolically,

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

Since there is an unequal sign in the alternative hypothesis, the test is two-tailed.

The value of the test statistic is equal to -1.64.

The two-tailed p-value for the test statistic value equal to -1.64 has the following expression:

\(P\left( {z < - 1.64} \right) + P\left( {z > 1.64} \right)\)

Referring to the standard normal distribution table, the left-tailed p-value when the z-score is equal to -1.64 is equal to 0.0505.

Referring to the standard normal distribution table, the left-tailed p-value when the z-score is equal to -1.64 is equal to 0.0505.

Thus, the p-value becomes:

\(\begin{array}{c}P\left( {z < - 1.64} \right) + P\left( {z > 1.64} \right) = 0.0505 + 0.0505\\ = 0.1010\end{array}\)

Therefore, the p-value is equal to 0.1010.