The manager of a department store is thinking about establishing a new billing system for the store's credit customers. After a thorough nancial analysis, she determines that the new system will be cost-eective only if the mean monthly account is more than $170. A random sample of 400 monthly account is drawn, for which the sample mean is $176 and the sample standard deviation is $50. Hint z0.1 = 1.28, z0.05 = 1.64, z0.025 = 1.96, z0.01 = 2.33 and z0.005 = 2.58. (a) Set up the hypotheses. (Remember that the manager would not want to introduce the new system without enough evidence for its cost-eectiveness.) (b) Find the critical value for this test using α = 1%. Is H0 rejected? (c) Find the p-value for this test. Is H0 rejected at 10%? (d) Suppose that the actual mean monthly account is $180, which makes the new billing system cost-eective. What is the probability that the manager decides not to change to the new billing system by this test at α = 1%? (e) Suppose that the actual mean monthly account is $165, which makes the new billing system not eective. What is the probability that the manager decides to change to the new billing system by this test at α = 10%?
The manager of a department store is thinking about establishing a new billing system for the store's credit
customers. After a thorough nancial analysis, she determines that the new system will be cost-eective only if
the mean monthly account is more than $170. A random sample of 400 monthly account is drawn, for which the
sample mean is $176 and the sample standard deviation is $50.
Hint z0.1 = 1.28, z0.05 = 1.64, z0.025 = 1.96, z0.01 = 2.33 and z0.005 = 2.58.
(a) Set up the hypotheses. (Remember that the manager would not want to introduce the new system without
enough evidence for its cost-eectiveness.)
(b) Find the critical value for this test using α = 1%. Is H0 rejected?
(c) Find the p-value for this test. Is H0 rejected at 10%?
(d) Suppose that the actual mean monthly account is $180, which makes the new billing system cost-eective.
What is the probability that the manager decides not to change to the new billing system by this test at
α = 1%?
(e) Suppose that the actual mean monthly account is $165, which makes the new billing system not eective. What
is the probability that the manager decides to change to the new billing system by this test at α = 10%?
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