2) Rosa is collecting beetles for her entomology class. The area has two species

Question

2) Rosa is collecting beetles for her entomology class. The area has two species of beetles that look nearly identical except for size, and we’ll call these species “little-type” and “big-type” beetles. Rosa needs to collect little-type beetles and wants to avoid collecting big-type beetles. As a species, big-types weigh an average of 1.2 ounces with a standard deviation of 0.2 ounces, and the weights follow a normal distribution. Rosa knew that this meant she could filter out about 98% of the big-type beetles that she found if she only collected beetles that weighed less than 0.8 ounces, so that’s what she did. A) This example can be thought of as a Null Hypothesis Significance Test (NHST). In these terms, when Rosa samples a beetle and decides whether or not to collect it, what is the null hypothesis and what is the alternative hypothesis? B) In 1-3 sentences, explain how you know which hypothesis is which for this example. C) Which part of the problem serves as the critical value? D) Imagine she finds a beetle and weighs it. What outcome in this example would be considered a significant result for a hypothesis test? What outcome would be considered a nonsignificant result? E) In 1-3 sentences, explain how you can tell which results count as significant and nonsignificant.

Explanation / Answer

A)

Null Hypothesis H0: The weight of beetle is greater than or equal to 1.2 ounces.

Alternative Hypothesis H1: The weight of beetle is less than 1.2 ounces.

B)

Null Hypothesis is for “big-type” beetles. If mean weight of collected beetles greater than 1.2 ounces then we accept the null hypothesis and conclude that the we have collected “big-type” beetles.

Alternative Hypothesis is for “little-type” beetles. If mean weight of collected beetles less than 1.2 ounces then we accept the alternative hypothesis and conclude that the we have collected “little-type” beetles.

C)

Rosa knew that this meant she could filter out about 98% of the big-type beetles that she found if she only collected beetles that weighed less than 0.8 ounces. So, the critical value is 0.8 ounces. If the mean weight of collected beetles less than 0.8 ounces then we accept the alternative hypothesis and conclude that the we are 98% confident that we have collected “little-type” beetles.

D)

If weight of beetles is less than 0.8 ounces, then the result is significant for a hypothesis test. If weight of beetles is greater than 0.8 ounces, then the result is non-significant for a hypothesis test.

E)

If weight of beetles is less than 0.8 ounces, then at 98% confidence level we know that collected beetle is of "little type" and the mean weight of collected beetles is less than 1.2 ounces and we can reject the null hypothesis. So, the result is significant for a hypothesis test.

If weight of beetles is greater than 0.8 ounces, then at 98% confidence level we do not know that collected beetle is of "little type" and the mean weight of collected beetles is greater than or equal to 1.2 ounces and we fail to reject the null hypothesis. So, the result is nonsignificant for a hypothesis test.

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