A manager claims that the defects in units produced at Site A are more than the defects in units produced at Site B. The sample of 23 units from Site A contain a mean of 78 defects and a standard deviation of 6 defects. The sample of 19 units from Site B contain a mean of 75 defects and a standard deviation of 4 defects. At \(\alpha=0.05\), can you support the manager's claim? Assume the population variances are equal.

(a) identify the claim and state H₀ and H_a,

(b) find the critical value(s) and identify the rejection region(s),

(c) find the standardized test statistic t,

(d) decide whether to reject or fail to reject the null hypothesis, and

(e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.