The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor’s degree or higher (The Wall Street Journal). A random sample of 120 employees in the private sector showed that 33 have a bachelor’s degree or higher. Does this indicate that the percentage of employees holding bachelor’s degrees or higher in the private sector is less than that in the federal civilian sector? Use α = 0.05.
Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetrical for problems with small samples that involve testing a mean.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.