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Mathematics, 05.08.2020 19:01 zwbaby3693

Suppose Ally is an energy efficiency consultant who is doing research for a hardware store that claims to promote energy efficiency. She wants to determine if the hardware store sells a higher proportion of LED light bulbs than the national average of 10.2%. She uses a computer program to select 60 calendar days from the previous year at random and obtains the stores sales records for those days. During those days, the hardware store sold 115 light bulbs, and 17 of them were LED. She performs a one‑sample zz ‑test for a proportion, using a significance level of =0.05.. She calculates a z ‑statistic of 1.624 and a P-value of 0.052. Based on her test result, she decides to fail to reject her null hypothesis and concludes that there is insufficient evidence to suggest that the amount of LED light bulbs that the hardware store sells is higher than the national average. Determine how changes to each of the following test conditions influence the z ‑statistic, P-value, decision, and conclusion of Ally's test. Assume that all of the other test conditions remain the same.

a. Ally uses a significance level of α= 0. 10 instead of α= 0.05.
b. Ally uses a two-tailed test instead of a one-tailed test and keeps the significance level at α= 0.05.
c. Ally increases her sample size to 128 light bulbs and the proportion of successes in her sample remains the same.

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