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?

Question

Advanced Placement (AP)

Dahlia Tanner

17 November, 08:51

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?

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Alijah Flowers · Answer 1

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.