Your Babysitter Claims She Is Underpaid Given The Current Ra

Your Babysitter Claims That She Is Underpaid Given the Current Market

Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.

Paper For Above instruction

The issue of fair wages and compensation in the context of the current market conditions is a significant concern for employers and employees alike. In this scenario, the babysitter claims to be underpaid, prompting a comparison between her current wage and the average market wage in her area. To evaluate this claim objectively, we can utilize the statistical concept of the Z score, which measures how many standard deviations a particular data point is from the mean of a distribution. This calculation helps determine whether her wage is notably below the market average or within the typical range of variation.

The babysitter's hourly wage is $12, while the average wage in the area is $14, with a standard deviation of 1.9. The formula to calculate the Z score is:

Z = (X - μ) / σ

Where:

  • X = her current wage ($12)
  • μ = average wage ($14)
  • σ = standard deviation (1.9)

Substituting these values:

Z = (12 - 14) / 1.9 = (-2) / 1.9 ≈ -1.05

The Z score of approximately -1.05 indicates that her wage is about 1.05 standard deviations below the mean wage of $14. To interpret this statistically, we consult the standard normal distribution table, which provides the probability associated with this Z score.

Looking up Z = -1.05 in the standard normal table, we find an area (probability) of approximately 0.1464. This value represents the proportion of wages that are below her current wage in the market distribution.

This means that roughly 14.64% of the wages are lower than her wage, suggesting that her compensation is below the typical range but not in an exceedingly rare or extreme position. In statistical terms, her wage is somewhat below the mean but still within a reasonable variation in the market.

Should you give her a raise? The decision should be based not only on the statistical analysis but also on other factors such as her performance, reliability, the local cost of living, and your budget as an employer. Statistically, since her wage falls below the mean and only about 15% of wages are lower, providing her with a raise to match or approach the average wage of $14 per hour would be reasonable and fair. Doing so would bring her closer to the typical market rate, aligning compensation with industry standards and possibly increasing her motivation and satisfaction.

In conclusion, the statistical analysis indicates that her current wage of $12 per hour is below the average in the area, positioned approximately 1.05 standard deviations below the mean, with about a 14.64% chance that wages are below this level. Therefore, from a data-driven perspective, giving her a raise to at least $14 per hour would be justified to ensure fair compensation and maintain good employment relations.

References

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