statistics one

Hypothesis:

According to Heathline.com say that men older than 19 years must drink an average 13 cups of water per day. I believe that the actual mean is less than that.

Data collection:

The population is students from Johnson and Wales and the sample is the 50 Johnson and Wales students.

Ratio:

Ratio because it is highest level of measurement and has a true zero.

Skewness is a measure of asymmetry of a data set relative to the mean. A data set in which the mean is greater than the median is skewed to the right while a data set in which the mean is less than the median is said to be skewed to the left. We can also determine the skewness of a data set by observing its graph or by calculating the skewness coefficient.

For the data set of the number of glasses of water drank per day, we can determine the skewness by first generating a histogram using Excel. From the shape of the histogram generated by Excel, it seems that the data is slightly skewed to the right. We also compare the mean and the median, and notice that the mean is 8.2, which is greater than the median which is 8.0, and therefore indicating a slight skewness to the right. We can also determine the skewness by observing the skewness coefficient in the Descriptive Statistics table generated by Excel’s Data Analysis Tool Pak. The coefficient of skewness is 0.5444 (to 4 decimal places). We notice that the value of the skewness coefficient. We determine if this skewness coefficient is statistically significant for the distribution. Data is generally said to be highly skewed if it has a coefficient of skewness that is outside the range of -1 to +1 (Ekstrom, 2012; Rayner, 1995). Significantly right-skewed data have coefficient of skewness values more than +1 while significantly less-skewed data have coefficient of skewness less than -1. (Rayner, 1995). The coefficient of skewed data in this case is within the range for a data set that is not skewed.

The value of the coefficient of skewness in this case is not statistically significant. Since the coefficient is a positive value but less than +1, the conclusion we can make is that the data is not skewed and is approximately normal. If we became stricter with our conclusion, then we can say that the data is only slightly skewed to the right (slightly positively skewed).

References

Ekstrom, M. (2012). A general measure of skewness. Statistics & Probability Letters, 82(8),

1559-1568.

Rayner, J.C.W. (1995). Interpreting the skewness coefficient. Communications in Statistics –

Theory and Methods, 24(3), 593-600.