Blue Crabs A marine researcher claims that the stomachs of blu...

Question

Blue Crabs A marine researcher claims that the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location. The stomach contents of a sample of 25 blue crabs from Location A contain a mean of 320 milligrams of fish and a standard deviation of 60 milligrams. The stomach contents of a sample of 15 blue crabs from Location B contain a mean of 280 milligrams of fish and a standard deviation of 80 milligrams. At , α= 0.01can you support the marine researcher’s claim? Assume the population variances are equal.

Accepted Answer

Hello, everyone, let's take a look at this question together. A nutritionist believes that the average protein content in the diet of wolves from forest M is higher than that of wolves from forest N. A sample of 20 wolves from forest M has a mean protein intake of 150 g with a standard deviation of 30 g. A sample of 22 wolves from forest N as a mean of 135 g with a standard deviation of 40 g. At alpha equals 0.01, can you support the nutritionist's claim? Assume equal population variances? Is it answer choice A? Yes, because the test statistic exceeds the critical value. Answer choice B, no, because the protein intake enforced N is significantly higher. Answer choice C no, because there is not enough evidence at the 0.01 level to support the nutritionist's claim, or answer choice D yes, because the sample means are different and we assume equal variances. So in order to solve this question, we have to recall how to test a claim so that we can determine whether we can support the nutritionist's claim that the average protein content in the diet of wolves from forest M is higher than that of the wolves from forest N, given a sample of 20 wolves from forest M has a mean protein intake of 150 g with a standard deviation of 30. Grams and a sample of 22 wolves from forest N as a mean of 135 g with a standard deviation of 40 g. And so the first step in determining whether we can support this claim is to state the hypothesis, starting with the null hypothesis, which is the population mean from forest M is equal to the population mean of forest N. And then our alternative hypothesis is the population mean from forest M is greater than the population mean from forest N, and then we calculate the pooled standard deviation using the formula for the pooled standard deviation, which is equal to the square root of in the numerator the sample size N from forest M subtracted by 1. Multiplied by the sample variants of forest M plus the sample size of forest and subtracted by 1 multiplied by the sample variants from forest N divided by the sample size M plus the sample size N subtracted by 2, and then we plug in our values into the formula for the pooled standard deviation, which gives us a Approximately 35.63 as the value for the pooled standard deviation. And then we calculate the test statistic, which is T is equal to sample mean 1 subtracted by sample mean 2, divided by our pooled standard deviation multiplied by the square root of 1 over sample size M plus 1 over sample size N. And substituting our values into the formula for the test statistic. We calculate approximately 1.36 as the value for our test statistic P. And then we find the critical value for alpha equals 0.01, as this is one tailed, and the degrees of freedom equals 40. And using the standard normal table, our critical value for our T is approximately 2.423. And then we compare our test statistic to the critical value. And since 1.36 is less than 2.423, we failed to reject the null hypothesis. So in conclusion, at the 0.01 significance level, there is not enough evidence to support the nutritionists claim that the wolves from forest M have a higher protein intake than those from forest N. Therefore, looking at our answer choices, we can identify that answer choice C is the correct answer, as we know that we cannot support the nutritionist's claim because there is not enough evidence at the 0.01 level to support the nutritionist's claim. So answer choice B is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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