Answer :
To test whether the average weight of bears in Yellowstone National Park is different from 187lb, we can use a hypothesis test.
(a) The test statistic for this hypothesis can be calculated using the formula:
test statistic = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 188.6lb, the hypothesized mean is 187lb, the sample standard deviation is 8.6lb, and the sample size is 46. Plugging these values into the formula, we get:
test statistic = (188.6 - 187) / (8.6 / sqrt(46))
(b) The critical value can be found using the significance level (α) and the degrees of freedom. In this case, since we're conducting a two-tailed test, the significance level is divided by 2. The degrees of freedom can be calculated as (sample size - 1).
(c) The p-value can be found by comparing the test statistic to the appropriate distribution (in this case, the t-distribution with the degrees of freedom calculated in (b)). The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
(d) To draw a conclusion regarding the hypothesis test, we compare the p-value to the significance level (α). If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Now, let's analyze the given answer choices:
(A) Incorrect: This answer is incorrect because it compares the critical value to the p-value, instead of the other way around.
(B) Incorrect: This answer is incorrect because it compares the p-value to 0.07, rather than the other way around.
(C) Incorrect: This answer is incorrect because it suggests that we cannot conclude when the p-value is less than 0.07, which is not accurate.
(D) Incorrect: This answer is incorrect because it compares the critical value to the p-value, instead of the other way around.
(E) Incorrect: This answer is incorrect because it suggests that we cannot conclude when the test statistic is greater than the p-value, which is not accurate.
(F) Incorrect: This answer is incorrect because it suggests that we cannot conclude when the test statistic is greater than the critical value, which is not accurate.
(G) Incorrect: This answer is incorrect because it compares the test statistic to the p-value, instead of the other way around.
(H) Correct: This answer is correct because it compares the p-value to the significance level, which is the correct way to draw a conclusion in a hypothesis test.
Therefore, the correct way to draw a conclusion regarding the above hypothesis test is: "If the answer in (c) is less than 0.07 then we conclude at the 7% significance level that the average weight of a bear in Yellowstone National Park is different from 187lb."
To know more about National Park refer here:
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