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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 1Machine 2x¯¯¯1=12.524x¯¯¯2=12.518n1=244n2=251Select 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.

Question

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.

check_circleAnswer
Step 1

Given
Null hypothesis H0:  µ1 = µ2
Alternative hypothesis Ha :  µ1 ≠ µ2

Sample mean number of cola bottles filled by machine 1 = 12.524
Sample mean number of cola bottles filled by machine 2 = 12.518
Standa...

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