The Human Resources Manager of a factory tries to reduce the staffing costs by hiring and laying off assembly line workers. He needs to hire and train new workers. However, newly hired workers are not as productive as experienced workers. The delivery schedule of products is based on the belief that trainees will achieve more than 90% of the level of experienced workers within 1 week of hiring. It is known that experienced workers assembled 500 products per day on average. Production records of a randomly selected day for a random sample of trainees give the number of products assembled as shown below. Hypothesis testing will be performed to determine whether the delivery schedule should be further adjusted.

509 442 508 501 470 499 444 477 418 416

410 465 432 440 485 415 481 445 465 424

515 449 405 444 469

Provide your numerical answers (corrected to 4 decimal places) of the following questions

a) Sample mean

b) Standard error estimate of the mean

c) Test statistic

d) p-value