Assume Coca Bottling is a company producing power drinks. You visited the company and did a sampling of 15 bottles to figure out the average volume of the bottle. You recorded the following data: 17, 16, 17.5, 16.7, 17.3, 15, 17.2, 17, 17.2, 16.8, 17.3, 16.9, 17.4, 17.7, 17.1
a- Find the mean, median mode of the data
b- If the population is normally distributed with a standard deviation of .4 , can we conclude that the average volume is approximately 17
c- How would your answer to the above question if we don't know the population standard deviation
d- How would your answer to part b and c change if we are interested in the average being at least 17
Assume that all answers should be given at a 98% confidence level
We do not do your work for you. However, in case you don't know the basics:
A. To find the mean (μ), add the scores and divide by the number of scores (n).
μ = ΣX/n
Arrange the scores in order of value. The middle-most score will be the median, that score which 50% ofthe scores have a value below it and 50% have a value above.
The mode is the most frequently observed score.
B. Use the Z-score = (X-μ)/SD
Are you sure you aren't looking for the 99.8% confidence level, which would be ±3 standard deviations (SD)?
Now that I've got you started, let's see what you can do.
I hope this helps. If not, repost with new or remaining questions. Thanks for asking.
a) To find the mean, median, and mode of the data, follow these steps:
Mean: Add up all the values and divide by the total number of values.
In this case, the sum of the values is 17 + 16 + 17.5 + 16.7 + 17.3 + 15 + 17.2 + 17 + 17.2 + 16.8 + 17.3 + 16.9 + 17.4 + 17.7 + 17.1 = 255.9
The total number of values is 15.
So, the mean (average) is 255.9 / 15 = 17.06.
Median: Arrange the values in ascending order and find the middle value. If there are two middle values, take their average.
In this case, after arranging the values in ascending order, we have:
15, 16, 16.7, 16.8, 16.9, 17, 17, 17.1, 17.2, 17.2, 17.3, 17.3, 17.4, 17.5, 17.7
There are 15 values, so the middle value is the 8th value, which is 17.1.
Thus, the median is 17.1.
Mode: Identify the value that appears most frequently.
In this case, there is no value that appears more than once. Therefore, there is no mode.
b) To determine whether we can conclude that the average volume is approximately 17, given a normally distributed population with a standard deviation of 0.4, we can perform a hypothesis test.
Null hypothesis: The true population mean is equal to 17.
Alternative hypothesis: The true population mean is not equal to 17.
Using the given data, we can perform a t-test or z-test. Since the sample size (15) is small and the population standard deviation (0.4) is provided, it is more suitable to conduct a t-test.
Using a t-test, we can calculate the t-value and compare it to the critical value at a 98% confidence level. If the calculated t-value falls within the critical region, we reject the null hypothesis.
c) If we don't know the population standard deviation, we would need to estimate it using the sample standard deviation. In this case, we would calculate the t-value using the sample standard deviation and compare it to the critical value at a 98% confidence level.
d) If we are interested in the average being at least 17, we would set up the null and alternative hypotheses accordingly:
Null hypothesis: The true population mean is less than or equal to 17.
Alternative hypothesis: The true population mean is greater than 17.
With the given information, we can again perform a t-test or z-test, depending on whether the population standard deviation is known or unknown. The calculations and conclusions would be the same as in parts b and c, but the alternative hypothesis would change to reflect the desired average being greater than 17.