To compare customer satisfaction with holiday gift purchases of digital gear from online and walk-in retailers, a researcher randomly selects 30 customer ratings of online retailers and 31 customer ratings of walk-in retailers. The mean customer rating of online retailers is 90 out of 100. Assume the population standard deviation is 3.4. The mean customer rating of walk-in retailers is 88 out of 100. Assume the population standard deviation is 3.5. At α = 0.01, can the researcher support the claim that the mean customer rating of online retailers is greater than the mean customer rating of walk-in retailers?

(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 z, 

(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.