When Yellowstone National Park was created in 1872, gray wolf populations were a

Question

When Yellowstone National Park was created in 1872, gray wolf populations were already in decline in Wyoming and neighboring states, and by 1926, all wolves in the park had been killed. During the mid-1900's, a campaign began to reintroduce the gray wolf. An extensive poll conducted in 1985 at Yellowstone National Park showed that 60% of visitors favored reintroducing them. A random sample of 350 visitors to the park this year found that 224 people were in favor of the reintroduction. At the 5% level of significance, does this provide sufficient evidence to support the claim that the proportion of visitors who support the reintroduction of wolves in Yellowstone National Park has increased since 1985? State the null and alternative hypothesis. Step 2: Prepare (check conditions to apply the Central Limit Theorem). Step 3: Compute d the value of the test statistic, sketch the appropriate distribution, label both the test statistic and the p-value). Step 4: Interpret (state your conclusion in the context of the application).

Explanation / Answer

34)

Null hypothesis: P <= 0.60
Alternative hypothesis: P > 0.60

35)

Because the sample is large we can use z distributed as the normal distribution if H0 is true.

With alpha = .05 the critical z score is 1.645. We reject H0 if z > 1.645.

36)

p = 224/350 = 0.64

= sqrt[ P * ( 1 - P ) / n ]

= sqrt [(0.60 * 0.40) / 350]

= 0.026

z = (p - P) /

= (.64 - .60)/0.026

= 1.538

p value is calculated using z = 1.538

p value = 0.062024.

37)

we fail to reject the null hypothesis

It does not provide sufficient evidence to support that claim

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