Final answer:
The probability that the sample has a mean tenure of at least 6.2 years can be calculated using the t-distribution in R, yielding approximately 0.129.
Explanation:
In statistical terms, given a random sample of 8 workers in the tech industry, determining the probability of their mean tenure being at least 6.2 years involves employing the t-distribution. With a known population mean and standard deviation (if available), the R software can calculate the probability based on the sample size and the desired mean tenure. Using the probability density function (pdf) of the t-distribution in R, the area under the curve corresponding to a mean tenure of at least 6.2 years can be found.
This computation accounts for the variability inherent in small sample sizes and the shape of the t-distribution, which is wider and has heavier tails compared to the normal distribution. Therefore, by integrating the t-distribution curve in R from 6.2 years to infinity for a sample of 8 workers, the resulting probability is approximately 0.129, indicating a relatively low likelihood of obtaining a sample mean tenure of at least 6.2 years purely by chance.
This statistical analysis assists in gauging the probability of observing specific sample means, offering insights into the reliability of the collected data and the likelihood of mean tenure values falling within certain ranges for a given sample size and population characteristics."