In: Statistics and Probability
A machine that fills beverage cans is suppose to put 24 ounces of beverage in each can. The following amounts are the amounts measured in random sample of eight cans.
24.00 23.94 23.96 23.98 23.92 23.90 23.83 23.95
assume the sample is normal. Can you conclude that the mean volume differs from 24 ounces? Use α=0.1level of significance.
A. Yes the mean fill volume appears to differ from 24 ounces.
B. There is not enough information to draw a conclusion.
C. No. There is insufficient evidence to conclude that the mean fill volume differs from 24 ounces.
In this scenario our claim is that the mean volume of filling breavrage cans is different from 24 Ounces.
To test this claim we have the sample size of 8 cans. From the sample we computed the mean and Standerd deviation from the sample.
To test this claim we have to use t distribution because here the population standard deviations is unknown and sample size is small.
Further the one sample t test is performed at 0.01 level of significance as below,
The sample size is n=8. The provided sample data along with the data required to compute the sample mean Xˉ and sample variance s^2 are shown in the table below:
X | X2 | |
24.00 | 576 | |
23.94 | 573.1236 | |
23.96 | 574.0816 | |
23.98 | 575.0404 | |
23.92 | 572.1664 | |
23.90 | 571.21 | |
23.83 | 567.8689 | |
23.95 | 573.6025 | |
Sum = | 191.48 | 4583.093 |
The sample mean \bar XXˉ is computed as follows:
The t critical value is calculated using t table or using Excel at 7 degrees of freedom.
Conclusion : the p value is greater than alpha level of significance 0.01 so we fail to Reject Ho null hypothesis. Therefore the corret option is C.
C. No. There is insufficient evidence to conclude that the mean fill volume differs from 24 ounces.
At 0.01 level of significance our result is not significant.
Thank you.