Question 1
Difference between inferential statistics and descriptive statistics
Descriptive statistics gives a simple summary concerning the collected data. It also summarizes preliminary observations made by a researcher (Queirós, Faria & Almeida, 2017). The summary made may contain numerical values or visuals. Therefore, descriptive statistics portray a simple quantitative component. On the other hand, inferential statistics refers to the gathering conclusion from data subjected to random variation. Inferential statistics are used to describe a system of processes used to highlight conclusions from various datasets obtained from processes affected by random variation. In other words, the inferential statistical processes employed depends on various collected data and its distribution (Bettany‐Saltikov & Whittaker, 2014).
Inferential statistics play a significant role in formulating theories in light of the researcher’s findings, while descriptive statistics, on the other hand, assist the researcher in mapping specific information that has been obtained. Inferential statistics allows investigators to utilize their findings from a small sample to inform letter concerning a larger population (Cranmer et al., 2017). In calculating certainty, descriptive statistics allow a researcher to measure the group assigned an experiment only. Therefore, the researcher may not factor in variables. Inferential statistics allow the researcher to account for error involved in sampling. Depending on the size of the data needed, a further test may be done on a larger population. Descriptive statistics, the research is, therefore, likely to get definitive calculations. Considering that the researcher is testing variables only using inferential statistics, drawing conclusions for descriptive statistics becomes easier. Therefore, descriptive statistics permit the simplicity of calculations.
For descriptive statistics, the researcher can summarize and graph connected data concerning a chosen group hence enhancing understanding of a given set of observations. Descriptive statistics describe a sample straightforwardly since it involves recording editor concerning the set and summarizing and graphing group properties (Ghauri, Grønhaug & Strange, 2020). With descriptive statistics, researchers minimize and fatalities Sims how they describe items or people they actually measure. The researcher does not stray from informing properties concerning a larger population. In descriptive statistics, the researcher collects large data and summarizes its too few meaningful graphs and values. Graphs in descriptive statistics real smooth vision and insight concerning the data. Descriptive statistics allows the researcher to view essential patents in given data set hands, making sense of the data. Unlike descriptive statistics, inferential statistics collects data for a smaller group and make inference for a larger population from that smaller group. Inferential statistics aims to generalize findings from a smaller group to predict the outcome of the general population.
Question 2
Confidence Interval
Confidence interval in statistics refers to an interval estimate calculated from statistics of data observed by the researcher. The confidence interval estimate gives a range for unknown parameters being investigated. In statistics, the confidence interval is essential because it gives a researcher the lower and upper limits of a sample (Motulsky, 2014). Confidence intervals are essential in our daily life. For instance,
Example 1
In the United States’ presidential election, the survey may indicate that the confidence level of the sitting President being re-elected is 94% with the modern error of + -2. The confidence interval indicates that if different surveys are conducted using the same techniques, the results remain within the limits of confidence level 94% of -2. Therefore, if 250 million votes turn out to vote, using the estimate confidence level, the confident interval for voters who will vote for the sitting president can be calculated as follows:
Confidence level = 94% +-2
Lower limit will be 94% – 2 = 92
92/100* 250,000,000 = 230,000,000
The upper limit will be 94% + 2 = 96
96/100* 2500,00,000 = 240,000,000
Therefore, the confidence interval will be 230,000,000 and 240,000,000
Example 2
For instance, in a clothing company, Gucci, making waist sizes for both male and female trousers, implement the use of confidence interval. Since waist sizes are manufactured using machines, they exist different error in sizes. For instance, if my friend and I bought jeans trouser manufactured by Gucci with waist size 32, if you use an elastic rope to measure the waist size, the sizes may be different with a certain margin. Although the jeans trousers are indicated waist size 32, a margin error of 0.5, we have been used in designing the size 32 waist. After measuring the waist size, confined it’s to be 31.7 for my trouser and 32.3 for my friend trouser, we may wonder why the company indicated waist size 32. According to Gucci, the company buys jeans trouser with waist size 32 has been given a range of measurements on both lower and upper limits of size 32. The estimated size within which the size 32 waist jeans trouser falls within indicates the company’s confidence interval.
The tag on the trousers read size 32 on 31.7 inches and 32 points 3 in jeans in this example. Therefore, the Gucci company assumes that any trouser with n 31.7 inches and 32.3 inches size waist is size 32, having a probability of 94 and 98% confidence interval.
Therefore, all the jeans trouser with waist size 32 will be within the confidence interval of 31.5 and 32.5
(32-0.5 and 32+0.5)
Question 3
Hypothesis Testing
Hypothesis testing in statistics refers to how researchers test and evaluate the results they obtain in an experiment or a survey and see if the results are meaningful (Murphy, Myors & Wolach, 2014). In everyday life, individuals test for new ideas routes to destinations faster and even new recipes.
Example one
Every day we are caught in between on which movie to watch on a Friday night. For instance, there are 2 movies that you would want to watch, but you’re not sure which one and therefore, you decide to ask for opinion and recommendation from Friends. Should you watch money heist or a game of thrones. From Friends recommendations, you find that the median for a game of throne movies, the center of distribution is 5, mean of 4.0, and a standard deviation of 0.6. money heist has a median of 3, a mean of 2.0, and a standard deviation of 0. 52. Depending on Friend’s recommendation, the movie’s evaluation is a statistical test used to decide on which movie you should watch. Hypothesis testing compares the movie, which has been recommended by most friends to assist in decision-making. In this real-life example, you decide to watch the game of thrones, as indicated by the hypothesis test.
Real-life example 2
A certain company specializes in automobile engine production. For the company to meet current environmental sustainability through protection by regulating emissions, it is essential to inspect the engines and indicate their average emissions. In this example, the machines should have an average of less than 20 PPM.
Below the emission levels
13.9, 12.7, 17.9, 16.6, 19.4, 16.4, 20.5, 22.5, 16.2 and 15.6.
Null hypothesis 1
Firm engine emissions fail to meet the standard for u>20.
Hypothesis 2
For u<20, firm engine emission meet the required standards.
We use t distribution and degree of freedom (df)= n-1
Therefore,
10-1= 9
Alternative false setting this example is u<20 and therefore,
Using the left-tail test, t=-3. Also, the value for p=0.00134
Regardless of the direction taken, a significant level is greater than the p-value, and t is less than 0, and therefore, the Null hypothesis is invalid.
The null hypothesis is valid, and therefore the emissions from company engines are standard.