Question

Civil Service: College Degrees: The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor’s degree or higher. 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 a= 0.05.

1. What is the level of significance? State the null hypothesis and alternate hypotheses.
2. Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
3. Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value
4. Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
5. Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student’s t table, use the closing d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more conservative answer. Answers may vary due to rounding.

Answer 1

a)

level of significance,

The null and alternative hypotheses are defined as,

b)

Here we will use z-distribution for the sample proportion

There are three main assumptions that need to be considered:

i) simple random sampling: The sample data values are drawn by simple random sampling

ii) Normality: The sample distribution of proportion to be approximately normal if,

iii) Independent of the case: the sample size should be 10% or less of the population (10% rule) when sampling is being done without replacement.

The z-statistic is obtained using the formula,

Where,

c)

The p-value is obtained from z-distribution table for z = -1.94

The colored area is correspond to p-value for z value = -1.94

d)

Since the P-value is 0.0262<0.05 at 5% significant level, the null hypothesis is rejected hence the difference in sample and population proportion is statistically significant at 5% significant level.

e)

Since the null hypothesis is rejected we can conclude that the difference in sample and population proportion is statistically significant at 5% significant level which mean the civil service employees have significantly higher degree compare to private sector employees