Question

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 bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break.

1495 1499 1502 1500 1491    1498    1498    1495 1488 1516

1513 1486 1504 1503 1493    1504    1489    1500 1495 1499

1501 1507 1511 1496 1486    1497    1510    1504 1493 1482

1511 1502 1520 1514 1486    1514    1500    1505 1512 1500

1504 1498 1503 1514 1474    1489    1488    1506 1517 1490

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 are the appropriate hypotheses?

b) What is the critical value for a test with a level of significance of 0.01?  

c) What is the value of the test statistic?

d) What is the p-value of the test?

e) True or False: the null hypothesis will be rejected at 5% level of significance.

f) True or False: the null hypothesis will be rejected at 1% level of significance.

g) True or False: you can conclude that 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 when allowing for a 1% probability of committing a Type I error.

h) True or False: you can 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 more than 1500 when allowing for a 1% probability of committing a Type I error.

Answer 1

a. Since we 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 so

e. Since p-value=0.4888>0.05 we accept null hypothesis. False: the null hypothesis will be rejected at 5% level of significance.

f. Since p-value=0.4888>0.01 we accept null hypothesis. False: the null hypothesis will be rejected at 1% level of significance.

g) False: you can conclude that 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 when allowing for a 1% probability of committing a Type I error.

h) False: you can 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 more than 1500 when allowing for a 1% probability of committing a Type I error.