One-Sample T-Tests - Essay Example

Inferential statistics is the branch of statistical studies in which we work out the variation of data (or sample data) hypothetically. To test the variability of data inferential statisticians have introduced several methods like z-series and t-tests. However, the t-Test is simpler in the sense that it does not require many calculations and the availability of complex statistical numbers like the standard deviation of a population. t-Test can deduce the depth of variation in the dataset based on a simple mean value. So, in essence, z-series and t-Test are the same but used in different conditions, z-series are used when the standard deviation is known for a dataset otherwise t-Test can help us out in assessing the variation of the dataset.

In this case, a study we are provided with the result of the survey which proclaims a mean value of eight shows being watched by the national population and we are required to formulate our opinion to hypothesize a value that represents the number of shows being watched per week by our neighbourhood and perform one-sample t-Test on this data.

As the first step, we formulate our opinion on our neighbourhood and hypothesize two values, first Ha assumes that there will be a greater number of news-based TV shows being watched in our neighbourhood than the mean value of eight TV Shows and second H0 assumes that there will be an equal number of news based TV shows being watched in our neighbourhood. Secondly, the random roll of a pair of dice has resulted in 7, 11, and 9, which gives us the value of 9.0 which represents the number of news-based TV shows being watched in our neighbourhood. Based on these findings and without performing any further calculations for the one-sample t-Test following interpretations were gathered.

The value of 9.0 suggests that there may be a close relationship between our neighbourhood and the national trend of watching news-based TV Shows. The value satisfies our hypothesis Ha.

The value of 9.0 also suggests that there may be only fewer chances of an occurrence of H0 or we may say it is unlikely that a lesser number of new-based TV Shows are being watched in our neighborhood.

There is a chance of having a lower value in another instance of the roll of dice but it is equally probable to have an even further rise in the value. So the sample gathered by the roll of the dice three times sufficiently represents our neighbourhood population.

We can further strengthen our hypothesis only through complete calculation of the one-sample t-Test. Because it is important to have tobt and t­crit to determine whether or not our sample mean lies in the region of rejection. If tobt is greater than tcrit we can deduce that the data collected through the roll of the dice does not represent true value for our neighbourhood.