Inferential Statistics in Business

So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.

 Inferential statistics helps us to analyze predictions, inferences, or samples about a specific population from the observations that they make. “With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone” (Trochim, 2006). The goal for this type of data is to review the sample data to be able to infer what the test group may think. It does this by making judgment of the chance that a difference that is observed between the groups is indeed one that can be counted on that could have otherwise happened by coincidence. In order to help solve the issue of generalization, tests of significance are used. For example, a chi-square test or T-test provides a person with the probability that the analysis’ sample results may or may not represent the respective population. In other words, the tests of significance provides us the likelihood of how the analysis results might have happened by chance in a scenario that a relationship may not exist between the variables in regards to the population that is being studied.

At 5% level of significance, is there sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different?

• Provide at least two examples or problem situations in which statistics was used or could be used.

Testing allows the p-value that represents the probability showing that results are unlikely to occur by chance. A p-value of 5% or lower is statistically significant. The p value helps in minimizing Type I or Type II errors in the dataset that can often occur when the p value is more than the significance level. The p value can help in stopping the positive and negative correlation between the dataset to reject the null hypothesis and to determine if there is statistical significance in the hypothesis. Understanding the p value is very important in helping researchers to determine the significance of the effect of their experiment and variables for other researchers

The critical value represents the point on the scale of test statistic value in which the null

The LV team is eager to learn what statistical significance is and why it’s an important construct in the study and use of inferential statistics.

The null hypothesis was that the female and male shoe sizes have an equal mean while the alternative hypothesis was that female and male shoe sizes do not have an equal mean. With the degrees of freedom being 33, the t-statistic is -8.27. The probability that -8.27 is ≤-1.69 is 7.5×10-10 for the one-tailed test. Also, the probability that -8.27 is ≤ ±2.03. is 1.5×10-9 for the two-tailed test. Due to both probabilities being under the alpha value of 0.05, the null hypothesis is rejected, and the alternative hypothesis is accepted at the 95% confidence level.

(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have

In order to know whether the evidence of research studies are accurate, one must be able to have a fundamental understanding in statistical analyses to determine if such descriptions and findings within manuscripts and articles are presented correctly and explicitly (Sullivan, 2012). Proper use of statistics begins with the understanding of both descriptive and inferential statistics. Correct organization and description of data characteristics from the population sample being studied leads the researcher to identify a hypothesis and formulate inferences about such characteristics. It is with inferential statistics that researchers conduct appropriate tests of significance and determine whether to accept or reject the identified null

“Hypothesis testing is a decision-making process for evaluating claims about a population” (Bluman, 2013, p. 398). This process is used to determine if you will accept or reject the hypothesis. The claim is that the bottles contain less than 16 ounces. The null hypothesis is the soda bottles contain 16 ounces. The alternative hypothesis is the bottles contain less than 16 ounces. The significance level will be 0.05. The test method to be used is a t-score. The test statistic is calculated to be -11.24666539 and the P-value is 1.0.  The P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypothesis is true. The T Crit value is 1.69912702. The calculations show there is enough evidence to support the claim that the soda bottles do

In his 2013 book, Naked Statistics, Charles Wheelan explains a field that is commonly seen, commonly applied, and commonly misinterpreted: statistics. Though statistical data is ubiquitous in daily life, valid statistical conclusions are not. Wheelan reveals that when data analysis is flawed or incomplete, faulty conclusions abound. Wheelan’s work uncovers statistics’ unscrupulous potential, but also makes a key distinction between deliberate misuse and careless misreading. However, his analysis is less successful in distinguishing common sense from poor judgement, a gap that enables the very statistical issues he describes to perpetuate themselves.

You take a random sample of 51 reduced-fat cookies and test them in a lab, finding a mean fat content of 4.2 grams. You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams. A) You are 95% confident that the mean fat in reduced fat cookies is between 3.4 and 5 grams of fat. B) We are 95% confident that the mean fat in all cookies is between 3.4 and 5 grams. C) We are 95% sure that the average amount of fat in the cookies in this study was between 3.4 and 5 grams. D) 95% of reduced fat cookies have between 3.4 and 5 grams of fat. E) 95% of the cookies in the sample had between 3.4 and 5 grams of fat. Determine the margin of error in estimating the population parameter. 12) How tall is your average statistics classmate? To determine this, you measure the height of a random sample of 15 of your 100 fellow students, finding a 95% confidence interval for the mean height of 67.25 to 69.75 inches. A) 1.5 inches B) 0.25 inches C) 1.06 inches D) 1.25 inches E) Not enough information is given. 12) 11) 10)

Source: G. C. Britz, D. W. Emerling, L. B. Hare, R. W. Hoerl, & J. E. Shade. "How to Teach Others to Apply Statistical Thinking." Quality Progress (June 1997): 67--80.

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Statistics are also used for making informed decisions – and misused for other reasons – in all areas of business and government. Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both