{"id":144,"date":"2018-03-10T16:12:00","date_gmt":"2018-03-10T16:12:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/10\/hypothesis-testing-problem-question-3-in-a-packing-plant-a-machine\/"},"modified":"2020-11-05T13:46:03","modified_gmt":"2020-11-05T12:46:03","slug":"hypothesis-testing-problem-question-3-in-a-packing-plant-a-machine","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-problem-question-3-in-a-packing-plant-a-machine\/","title":{"rendered":"Hypothesis Testing Problem – Question 3 (In a packing plant, a machine…"},"content":{"rendered":"
\n
Question <\/span><\/b><\/span>
In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine would pack faster on the average than the machine currently used. To test the hypothesis, the time it takes each machine to pack ten carons are recorded. The result in seconds is as follows.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 New Machine<\/b><\/td>\nOld Machine <\/b><\/td>\n<\/tr>\n
 42.1<\/td>\n 42.7<\/td>\n<\/tr>\n
 41<\/td>\n 43.6<\/td>\n<\/tr>\n
 41.3<\/td>\n 43.8<\/td>\n<\/tr>\n
 41.8<\/td>\n 43.3<\/td>\n<\/tr>\n
 42.4<\/td>\n 42.5<\/td>\n<\/tr>\n
 42.8<\/td>\n 43.5<\/td>\n<\/tr>\n
 43.2<\/td>\n 43.1<\/td>\n<\/tr>\n
 42.3<\/td>\n 41.7<\/td>\n<\/tr>\n
 41.8<\/td>\n 44<\/td>\n<\/tr>\n
 42.7<\/td>\n44.1 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform  the required hypothesis test at the 5% level of significance.<\/p>\n

Solution Steps<\/b><\/span><\/span>
Download the excel sheet for this excercise for free<\/a>
<\/sub><\/p>\n

Just as before, we need to try to understand the question clearly so we can set up the null hypothesis and the alternate hypothesis.<\/p>\n

Note the following points about this question<\/p>\n