In contract negotiations, a company claims that a new incentive scheme has resulted in average monthly earnings of at least $12,000 for all customer service workers. A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of $11,440 and a standard deviation of $1,458. Assume a normal distribution. We are interested in whether the sample results show that the company's claim is invalid.

a) Do you recommend a hypothesis test with a one-sided alternative hypothesis or a two-sided alternative hypothesis? Justify your answer.

b) Is the Company's claim invalid? Explain why or why not? Your answer should be in the form of a hypothesis test at the 5% significance level.

c) Construct a 95% confidence interval for the average monthly earnings of all customer service workers.