Question

Consider a random sample of 5 adults over the age of 25 from a large population, which is normally distributed, where E represents the total years of education completed: ?= (10, 12, 12, 16, 20) Suppose that someone claims that the average person in the population is a college graduate (? = 16).

A. What is the null hypothesis?  What is the alternative hypothesis?

B. Can you reject the null hypothesis at the 10‐percent level of significance?   Can you reject the null hypothesis at the 5‐percent level of significance?   Use the critical value approach.  You can use R for critical values, but you must show all of your calculations and explain.  Use R, however, to check your work.

C. What is the 95‐percent confidence interval for years of education?  Provide a written interpretation explaining your answer.

Answer 1

a) H0: the average person in the population is a college graduate is 16 i.e. ? = 16

H1: the average person in the population is a college graduate is not 16 i.e. ? not = 16

Let the los be alpha = 10%

b)

From the given data

t Test
Test Statistic, t: -1.1180
Critical t: ±2.1318
P-Value: 0.3262
Here t value is in t critical values and P-value > alpha 0.10 so we accept H0

Thus we conclude that  the average person in the population is a college graduate is 16 i.e. ? = 16

c)

The 95‐percent chance that for years of education completed is lies between 9 and 19 years