Calculate The Sample Size Using A 95% Confidence Level

Calculate the sample size using a 95% confidence level, and a 5% margin of error

Calculate the sample size using a 95% confidence level, and a 5% margin of error. Place the calculation in the Appendix. Discuss how validity (and reliability) will be achieved. C’s Burgers, Fires & Shakes is looking to test their hypothesis that there is a correlation between employee productivity and increased sales. Hypothesis 1 states that there is no difference in sales based on the productivity of each shift. While Hypothesis 2 looks to prove that there is a difference in sales based on the productivity of each shift. The variable are the production of the workers on each shift reflected by hours worked (IV) and the amount of increased sales (DV). The population is the entire pool of 400 employees of all the C's Burgers, Fries, and Shakes locations. It will be time-consuming to test the whole of the population, so a sample of five random employees will be taken from 40 random stores for a total sample population of 200. The target population at C’s Burgers, Fries, and Shakes would be a random sample of five total employees aged (21–65) at a random store location. There will be 40 store locations selected with ten stores from the east, west, south, and north regions of the nation. Managers, shift supervisors, and new hires will be excluded. The reasoning in selecting this target population is to observe and track the productivity of the average C’s Burgers, Fries, and Shakes employee. Including managers, shift supervisors, and new hires in the population will probably cause a confounding effect due to their more than average and less than average productivity.

Paper For Above instruction

Determining an appropriate sample size is a critical step in conducting valid and reliable research. Using a confidence level of 95% with a 5% margin of error is standard practice in social science research, providing a balance between precision and feasibility. The sample size calculation hinges on the population size, the desired confidence level, and the acceptable margin of error. For a finite population, the sample size can be calculated using the following formula:

n = N  Z2  p  (1 - p) / [E2  (N - 1) + Z2  p  (1 - p)]

Where:

  • N = population size (400 employees)
  • Z = Z-score associated with the confidence level (for 95%, Z=1.96)
  • p = estimated proportion of the attribute present in the population (typically 0.5 for maximum sample size)
  • E = margin of error (0.05)

This formula ensures an accurate estimation of the sample size necessary to generalize the findings to the population with the desired confidence and precision.

Applying these values:

n = 400  (1.96)^2  0.5  0.5 / [0.05^2  (400 - 1) + (1.96)^2  0.5  0.5]

Calculating each component gives:

n ≈ 400  3.8416  0.25 / [0.0025  399 + 3.8416  0.25]


n ≈ 400 * 0.9604 / [0.9975 + 0.9604]


n ≈ 384.16 / 1.9579


n ≈ 196.4

Thus, a sample size of approximately 197 employees out of the population of 400 provides a 95% confidence level with a 5% margin of error.

In the study's context, selecting a sample of 200 employees aligns closely with this calculation, ensuring that the sample is statistically representative of the population. Random sampling from 40 stores across different regions further strengthens the representativeness, reducing potential bias.

Validity and reliability are essential for trustworthy research outcomes. Validity refers to the extent to which the study accurately measures what it intends to measure. To enhance validity, the research design incorporates random sampling, ensuring every employee has an equal chance of selection, thus representative of the entire population. Additionally, clearly defining operational variables like 'employee productivity' and 'sales increase' ensures consistent measurement across respondents and reduces measurement bias.

Reliability concerns the consistency and stability of the measurement instruments and procedures over time. To achieve reliability, standardized data collection protocols will be established, including uniform instructions for participants and consistent recording of variables like hours worked and sales figures. Pilot testing data collection methods may also be employed to identify and rectify issues that could compromise reliability.

Furthermore, employing validated measurement tools, such as standardized questionnaires or tracking systems for productivity and sales, will enhance the reliability of the data. Training data collectors thoroughly and implementing quality control checks throughout data collection will also minimize errors and ensure data consistency.

In conclusion, utilizing an accurately calculated sample size grounded in statistical principles, combined with rigorous methods to ensure validity and reliability, will strengthen the integrity of the research examining the correlation between employee productivity and sales at C’s Burgers, Fries & Shakes. Such methodological rigor allows the research findings to be confidently generalized to the broader population, providing valuable insights for strategic decision-making.

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