Advanced Placement (AP) College

Erica has a swimming pool at her house. Once a year she purchases a 50-pound bucket of chlorine pellets from an online company. Out of curiosity she weighs the bucket and finds that it only weighs 46.2 pounds. She purchases 4 more 50-pound buckets, giving her an SRS of size 5. The mean weight of the 5 buckets is 48.5 pounds. She suspects that the company is cheating the customers. She uses her data to test the hypotheses H0: \muμ = 50 pounds versus Ha: \muμ < 50 pounds. The P-value of her test is 0.0851. What decision should she make and what type of error could she make as a result of her decision?

Answers

Answer 1

Answer:

She should fail to reject the null hypothesis. She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is.

Explanation:

Answer 2

She should fail to reject the null hypothesis. She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is.

What is Type II error?

Karl Popper is arguably the most significant scientific philosopher of the 20th century (Wulff et al., 1986). Even scientists who don't typically read philosophy books are familiar with his main tenets on science.

Popper's philosophy has gained appeal in part because it has been succinctly described by people like Nobel Prize winner Peter Medawar (Medawar, 1969).

When empirical scientists (those who emphasize observations alone as the starting point of research) claim that science proceeds from observation to theory, Popper makes the crucial point that they are putting the cart before the horse because there is no such thing as a pure observation that does not depend on other sources of information.

Therefore, She should fail to reject the null hypothesis. She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is.

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