The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 50 bears has a mean weight of 188.8 lb with a standard deviation of 8.7 lb. At [tex]\alpha = 0.03[/tex], can it be concluded that the average weight of a bear in Yellowstone National Park is different from 187 lb?

(a) Find the critical value.

(b) Find the value of the test statistic for the above hypothesis.

(c) Find the p-value.

To test whether the average weight of bears in Yellowstone National Park is different from 187lb, we can conduct a hypothesis test using the sample data. The critical value is approximately ±2.462 at a significance level of 0.03. The test statistic value is approximately 1.301, and the p-value is approximately 0.199.

Explanation:

To determine whether the average weight of a bear in Yellowstone National Park is different from 187lb, we can conduct a hypothesis test.

(a) To find the critical value, we need to calculate the critical t-value with a significance level of 0.03 and degrees of freedom (df) equal to the sample size minus one (n-1). Using a t-table or a statistical calculator, the critical value is approximately ±2.462.

(b) The test statistic value can be calculated using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size)). Plugging in the values, we get t = (188.8 - 187) / (8.7 / sqrt(50)) ≈ 1.301

(c) The p-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. The p-value can be calculated using a t-distribution table or a statistical calculator. For a two-tailed test, we multiply the probability value by 2. In this case, the p-value is approximately 0.199.

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