A manufacturer of smoke detectors designed for fire protection claims that the average area that the smoke detector covers is at least 60 square meters. To test this claim, you randomly select a sample of 22 systems and find the mean coverage area to be 58 square meters. Assume the population standard deviation is 3.5 square meters. At α = 0.10, do you have enough evidence to reject the manufacturer’s claim?

(a) identify the claim and state H₀ and H_α.
(b) find the standardized test statistic z.
(c) find the corresponding P-value.
(d) decide whether to reject or fail to reject the null hypothesis.
(e) interpret the decision in the context of the original claim.