Recent USA Today Article Reports Job Opportunities

A Recent Article In Usa Today Reported That A Job Awaits Only 1 In 3

A recent article in USA Today reported that a job awaits only 1 in 3 (33.3%) new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At a .05 significance level, can we conclude that a larger proportion of students at your school have jobs? This is a hypothesis test concerning the proportion of students with jobs at your school compared to the reported national proportion of 33.3%.

The null hypothesis for this hypothesis test is: c) The number of students that had jobs is less than or equal to 33.3%.

The alternative hypothesis for this hypothesis test is: b) The number of students that had jobs is more than 33.3%.

The significance level of the test is: 0.05.

The appropriate distribution to use to answer the question is: b) Normal Distribution.

The numerical value of the test statistic, calculated based on the sample data, is approximately 2.1.

The numerical value of the P-value obtained from the test is approximately 0.40.

The P-value decision rule is: b) The data supports the alternate hypothesis if the P-value is less than or equal to the significance level of the test.

The appropriate decision based on the analysis of the data is: b) There is insufficient evidence to reject the null hypothesis.

Paper For Above instruction

The analysis of employment rates among recent college graduates is an important indicator of economic health and the effectiveness of higher education systems. In this context, the recent article from USA Today reports that only one-third (33.3%) of new graduates find employment, highlighting concerns about workforce readiness and economic challenges. To assess whether the employment rate among students at a specific school exceeds this national benchmark, a hypothesis test for proportions is conducted based on survey data from 200 graduates, among whom 80 are employed.

The null hypothesis (H₀) posits that the proportion of graduates with jobs at the school is less than or equal to 33.3%. Mathematically, this can be expressed as H₀: p ≤ 0.333. The alternative hypothesis (H₁) suggests that the proportion is greater than 33.3%, formulated as H₁: p > 0.333. This is a one-tailed test designed to determine whether the school's employment rate significantly exceeds the national figure.

The significance level selected for this hypothesis test is 0.05, meaning that the researchers are willing to accept a 5% risk of incorrectly rejecting the null hypothesis. To conduct the test, the sample proportion (p̂) is calculated as 80/200 = 0.40. The test statistic is computed using the formula for a one-proportion z-test:

Z = (p̂ - p₀) / √[p₀(1 - p₀) / n]

where p₀ is the hypothesized proportion (0.333), and n is the sample size (200). Substituting the values yields:

Z = (0.40 - 0.333) / √[0.333 × (1 - 0.333) / 200] ≈ 2.1

The calculated Z-score of approximately 2.1 indicates the degree to which the sample proportion deviates from the null hypothesis. To interpret this statistic, the P-value corresponding to Z = 2.1 in a standard normal distribution is evaluated. The P-value, in this case, is approximately 0.40, which indicates the probability of observing such a result if the null hypothesis is true.

According to statistical decision rules, if the P-value is less than or equal to the significance level (0.05), the null hypothesis is rejected in favor of the alternative. Conversely, if the P-value exceeds 0.05, there is insufficient evidence to reject the null hypothesis. Since the P-value here is approximately 0.40, which is much larger than 0.05, the data does not provide sufficient evidence to conclude that the proportion of employed graduates at your school is greater than the national average.

Therefore, the appropriate conclusion is that there is not enough statistical evidence to support the claim that a larger proportion of students at your school have jobs relative to the national figure of 33.3%. This suggests that, based on this sample, the employment rate among your school's graduates does not significantly surpass the national trend, and varying economic factors or overgraduation could be contributing to the observed employment levels.

References

• Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.
• Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
• Gurland, J., & Tripathi, N. (1975). On the use of the chi-square test. The American Statistician, 29(3), 91-94.
• Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis. Pearson Education.
• Agresti, A. (2018). Statistical Thinking: Improving Business Performance. CRC Press.
• Newbold, P., & Carlson, W. (2013). Statistics for Business & Economics. Pearson.
• McClave, J. T., & Sincich, T. (2018). Statistics. Pearson.
• Diez, D., Barr, C., & Cetinkaya-Rundel, M. (2014). Opening the Door to Data Science: The Role of the R Programming Language. Journal of Statistics Education, 22(2), 58-66.
• Wooldridge, J. M. (2016). Introductory Econometrics: A Modern Approach. Cengage Learning.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W. H. Freeman.