You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 50 water bottle to durability test and the following data is on the number of times the handles have been used to lift the bottles before they break. 1493 1506 1515 1491 1500 1505 1517 1510 1506 1503 1503 1491 1495 1496 1505 1493 1486 1504 1483 1496 1493 1490 1514 1494 1497 1501 1494 1494 1495 1510 1494 1486 1495 1506 1506 1507 1502 1498 1500 1505 1492 1486 1501 1496 1501 1521 1510 1510 1501 1498 Assume that the number of times the handles have been used to lift the bottles before they break follows a normal distribution. You want to test to see if there is enough evidence that the mean number of times the handles have been used to lift the bottles before they break is more than 1500. (a) What is the population of interest? (b) What is the parameter of interest? (c) State the appropriate hypotheses (d) What is the critical value for a test with a level of significance of 0.01? (e) What is the value of the test statistic? (f) What is the p-value of the test? (g) Will the null hypothesis be rejected at 5% level of significance? (h) Will the null hypothesis be rejected at 1% level of significance? (i) What is the conclusion? (i) Can we conclude that there is not enough evidence that the mean number of times the handles have been used to lift the bottles before they break is no more than 1500 when allowing for a 1% probability of committing a Type I error.