Table 1: Mock Data Set and Population mean of 30 nuts

Table 2: Radom Sampling Data Set and Sample means

Part I
Sample Mean Related to Population Mean

            The calculation for this assignment is performed on Microsoft Excel. A mean weight is calculated for all 30 nuts in table 1 that represents the population mean, i.e. 1.92. The sample means for nuts i.e. peanuts, almonds, and Brazil nuts are 0.19, 1.92, and 3.87 respectively. The computation procedure is same for both population mean and the sample mean i.e. dividing the summation of numeric values to a number of total values. However, notations for both means are different than each other, i.e. μ for the population mean and x̄ for sthe ample mean. To inferences, the formula for sthe ample mean and population mean is sthe ame with different notations that improves the population mean’s accuracy through increasing a number of the observations. Hence, both population and sample mean are sthe ame for the same data.

Sampling Strategy Impact Uncertainty

            A point estimate of the parameter is evaluated by statistical estimation; whereas variability related to the estimation is quantified by the interval estimation. Sampling plan implementation is useful to organize the data process, and it helps to improve the correctness of uncertainty aspects’ in a null hypothesis as well. A risk of uncertainty is improved by a sampling strategy by utilizing both statistical population and target population so that loops could get close between collecting, evaluating, and storing the data of sample population (Banerjee & Chaudhury, 2010). The probability of rejecting the null and confidence interval of the observations is included in this.

            One other way that sampling strategy can affect an uncertainty related to using samples to generate inference about the population is improving correctness of the process of assessment  (Surbhi, 2016). The random samples’ feasibility can be biased when the population in unidentified. The estimate of the parameters of random samples needs to be generated to get the unbiased result. For example, Microsoft Excel is used to generate random sampling in table 2 of the paper regardless of the nuts’ type, then mean for each sample is calculated as well as the population means. This information is useful for inference the harvesting nuts’ unbiased probability in a selected geographic location. Randomization could be further conducted to narrow down the nuts’ type that has the best chance to yield a harvest that is highly profitable with an unbiased statistical methodology. Sampling strategy affects a true mean effect connected with quantifying an estimated inference population sample’s variability (Taylor, 2017). Determining a sampling plan that is best to analyze a sample from the whole population would be more efficient.

Part II
Confidence Interval and Confidence Levels

The mean of the sample of all peanuts represents the mean of the whole population.                                                                                  Scale: 5

The mean of the sample of all Brazil nuts represents the mean of the whole population.                                                                             Scale: 5  

The mean of the last sample with a combination of types of nuts represents the mean of the whole population.                                          Scale: 10

The mean, +/- 2.3 grams, of the last sample with a combination of types of nuts represents the mean of the whole population.                                    Scale: 10

            For this exercise, it is assumed that the random dataset is being used; a sample mean (x̄ = Σ xᵢ / n) is used in the case where x̄ represents sample mean = Σ (summation) of xᵢ+x₂+x₃+…..+ x₁₄ divided by n (n represents the total number of observations). Hence, 14 random peanut sampling’s x̄ = .91; 9 random almond sampling x̄ = 1.91; and 7 random Brazil nut sampling x̄ = 4.11 for a population mean. The entire population is calculated by formula i.e., m = Σ xᵢ/N. The sampling accuracy’s confidence interval would be lowered by this. This is why, 5-poithe nt confidence level is used for the two statements i.e., the sampling mean for the peanut and sampling mean for Brazil nut represents the entire population’s mean. The population mean is estimated by calculating a sample mean. Then, an estimation is used for null hypothesis test and determine the sample population’ actual parameter. If all nuts are combined; it can be assumed that sampling mean will be calculated of the nuts’ whole population in a dataset. The mean, +/- 2.3 grams, of the last sample with types of nuts’ combination represent the entire population’s mean comprises of a confidence interval that is interpretable as testing the confidence interval of the H₀ (null hypothesis). It is assumed that no relation exits between the nuts’ group randomized in a sample dataset. Testing a theory is allowed by this via statistical testing to accept or reject the hypothesis. Hence, it can be assumed without any calculation that confithe dence level is higher for these statements.

References Generate Samples by Using Probability and Defining Variables

Banerjee, A., & Chaudhury, S. (2010). Statistics without tears: Populations and samples. Industrial Psychiatry Journal, 19(1), 60-65. doi:10.4103/0972-6748.77642

Surbhi, S. (2016, May 9). Difference between descriptive and inferential statistics. Key Differences. n.d. Retrieved March 7, 2018, from https://ncuone.ncu.edu/d2l/le/content/48143/fullscreen/316062/View

Taylor, C. (2017, May 23). What Level of Alpha Determines Statistical Significance? Retrieved March 5, 2018, from ThoughtCo.: https://www.thoughtco.com/inferential-statistics-4133531