An Engineers' Union In Columbus, Ohio, Claims That The Avera
An Engineers Union In Columbus Ohio Claims That the Average Pay For W
An engineers union in Columbus, Ohio claims that the average pay for women working in the auto industry is $16 per hour. A simple random sample of 9 women working in 1998 as engineers in the automotive industry in Columbus, Ohio revealed that the average pay rate was $15 per hour with a standard deviation of $2.
(a) Find a 99% confidence interval on the true mean pay rate of women engineers.
(b) What can you say about the union's claim? Write a sentence or two.
Paper For Above instruction
The assertion by the engineers union in Columbus, Ohio, that women in the auto industry earn an average of $16 per hour warrants statistical analysis to determine its validity. Based on a random sample of nine women engineers with a sample mean of $15 per hour and a sample standard deviation of $2, we can construct a 99% confidence interval to estimate the true mean pay rate. This interval provides a range within which the actual average pay is likely to fall, with a confidence level of 99%, thus offering insight into whether the union's claim holds statistical support.
To calculate this confidence interval, we recognize that the sample size is small (n=9), prompting the use of the t-distribution instead of the normal distribution. The degrees of freedom are n - 1 = 8. Referring to t-tables or using statistical software, the t-value for a 99% confidence level with 8 degrees of freedom is approximately 3.355. The formula for the confidence interval is:
CI = sample mean ± tcritical × (sample standard deviation / √n)
Plugging in the values:
- Sample mean (x̄) = 15
- Standard deviation (s) = 2
- Sample size (n) = 9
- tcritical ≈ 3.355
The standard error (SE) is:
SE = 2 / √9 = 2 / 3 ≈ 0.6667
The margin of error (ME) is:
ME = 3.355 × 0.6667 ≈ 2.237
Therefore, the 99% confidence interval is:
[15 - 2.237, 15 + 2.237] = [12.763, 17.237]
Based on this interval, which ranges from approximately $12.76 to $17.24 per hour, we observe that the claimed average of $16 per hour falls within this range. This suggests that the union's claim is statistically plausible; however, the interval's width indicates some uncertainty, and further data could improve precision.
Regarding the union's claim, the analysis shows that the true average pay for women engineers may be around $16, but the current sample data also support the possibility that it could be slightly lower or higher within the confidence interval. Thus, while the claim is consistent with the data, more extensive sampling would provide greater confidence in the estimate and either confirm or refute the union's statement definitively.
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