Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the amount of cola in the bottles filled by Machine 1 is the same as the amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Leah knows that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. Leah randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let α=0.05, μ1 be the population mean amount of cola in bottles filled by Machine 1, and μ2 be the population mean amount of cola in bottles filled by Machine 2. The test statistic is z≈3.33, and the rejection region is less than −z0.025≈−1.960 or greater than z0.025≈1.960. What conclusion could be made about the mean amount of cola filled in each bottle between the two machines? Identify all of the appropriate conclusions. Machine 1 Machine 2 x¯¯¯1=12.524 x¯¯¯2=12.518 n1=244 n2=251 Select all that apply: A) Fail to reject the null hypothesis. B) Reject the null hypothesis. C) There is insufficient evidence at the α=0.05 level of significance to conclude that the mean amount of cola in bottles filled by Machine 1 is different than the mean amount of cola in bottles filled by Machine 2. D) There is sufficient evidence at the α=0.05 level of significance to conclude that the mean amount of cola in bottles filled by Machine 1 is different than the mean amount of cola in bottles filled by Machine 2.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the amount of cola in the bottles filled by Machine 1 is the same as the amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Leah knows that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. Leah randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let α=0.05, μ1 be the population
| Machine 1 | Machine 2 |
|---|---|
| x¯¯¯1=12.524 | x¯¯¯2=12.518 |
| n1=244 | n2=251 |
Select all that apply:
A) Fail to reject the null hypothesis.
B) Reject the null hypothesis.
C) There is insufficient evidence at the α=0.05 level of significance to conclude that the mean amount of cola in bottles filled by Machine 1 is different than the mean amount of cola in bottles filled by Machine 2.
D) There is sufficient evidence at the α=0.05 level of significance to conclude that the mean amount of cola in bottles filled by Machine 1 is different than the mean amount of cola in bottles filled by Machine 2.
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