Questions: Before 1918 approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced.

Before 1918 approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced.
Transcript text: Before 1918 approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced.
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Solution

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Solution Steps

Step 1: Hypothesis Test for Male Wolves Proportion

We conducted a hypothesis test to determine if the proportion of male wolves has increased since 1918. The null hypothesis \( H_0 \) states that the proportion of male wolves is equal to 0.60, while the alternative hypothesis \( H_a \) states that the proportion is greater than 0.60.

The test statistic is calculated as follows:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} = 1.021 \]

The corresponding p-value for this test statistic is 0.154.

The critical region for a one-tailed test at a significance level of \( \alpha = 0.05 \) is defined as \( Z > 1.645 \).

Step 2: Hypothesis Test for Female Wolves Proportion

Similarly, we performed a hypothesis test for the proportion of female wolves. The null hypothesis \( H_0 \) states that the proportion of female wolves is equal to 0.40, while the alternative hypothesis \( H_a \) states that the proportion is less than 0.40.

The test statistic is calculated as:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} = -1.021 \]

The p-value for this test statistic is also 0.154.

The critical region for this one-tailed test at \( \alpha = 0.05 \) is defined as \( Z < -1.645 \).

Final Answer

For the hypothesis test of male wolves, we do not reject the null hypothesis since \( 1.021 < 1.645 \). For the hypothesis test of female wolves, we also do not reject the null hypothesis since \( -1.021 > -1.645 \).

Thus, the final conclusions are:

  • For male wolves: \( \text{Do not reject } H_0 \)
  • For female wolves: \( \text{Do not reject } H_0 \)

\(\boxed{\text{Do not reject } H_0 \text{ for both male and female wolves}}\)

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