***Your Name***
***Institution***
1.
Mean ounces = (14.5+14.6+14.7+14.8+14.9+15.5+14.8+15.2+15+15.1+15+14.4+15.8+14+16+16.1+15.8+14.5+14.1+14.2+14+14.9+14.7+14.5+14.6+14.8+14.8+14.6)/30
Sorting the dataset, the following is obtained:
14 14 14.1 14.2 14.4 14.5 14.5 14.5 14.6 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.8 14.9 14.9 14.9 15 15 15.1 15.2 15.3 15.5 15.8 15.8 16 16.1
Hence, median = (15-th data + 16-th data)/2 = (14.8+14.8)/2 = 14.8
Standard deviation = 8.78330 ≈0.54 ounce
Standard deviation of the mean = 0.5430
ZQ=Q-160.5430P-∞<x<Q=P-∞<X<ZQ=1-0.95 =>ZQ=-1.64=>Q=-1.640.5430+16≈15.84Confidence interval is (15.84, +∞)
3.
Since the company wants to test whether the bottles have a mean of less than 16 ounces, the test is:
Null hypothesis: μ=16
Alternative hypothesis: μ<16
Since the sample mean = 14.87 < 15.84, this means the null hypothesis is rejected.
The soda in the bottle is less than 16 ounces as claimed.
The three possible causes are:
- The machine responsible for filling in the soda was faulty.
- The bottles were exposed to the air before closing them, so some water in the soda evaporated causing the amount to be less than 16 ournces.
- Too little water was added into the soda mixture.
Strategies to avoid the deficit in the future include:
- Ensuring the machine is working properly.
- Ensure that the bottles are closed after filling them with soda.
- Ensure that the amount of water needed is increased.
