Question

According to data from the 2018 General Social Survey (GSS 2018), the average number of years of education of the 2345 adults in the U.S. sample is 13.73, with a standard deviation of 2.974. Compared to the national average of 13.26 years of education in 2000, researchers are wondering if the national education level had increased during these years. Do a hypothesis testing with α=0.05. Use this example to answer questions 24 to 27.

24. What’s the null hypothesis in this case?
A. The average number of years of education in the U.S. adult population did not change much from 2000 to 2018.
B. The average number of years of education in the U.S. adult population was equal to 13.73 in 2018.
C. The average number of years of education for the GSS 2018 sample is no different from 13.26, the national average in 2000.
D. The average number of years of education in the U.S. adult population had increased from 2000 to 2018.

25. What’s the alternative hypothesis in this case?
A. The average number of years of education in the U.S. adult population had changed since 2000.
B. The average number of years of education for the GSS 2018 sample is different from 13.26, the national average in 2000.
C. The average number of years of education in the U.S. adult population in 2018 was higher than that in 2000.
D. The average number of years of education in the U.S. adult population had decreased from 2000 to 2018.

26. Which of the following statements about this example is correct?
A. This is a two-tailed test and you have two rejection regions.
B. Since the sample size is large, we cannot use the normal distribution as the sampling distribution.
C. This is a one-tailed test and the rejection region is on the left side of the sampling distribution.
D. The rejection region is on the right side of the sampling distribution.

27. What conclusion can we draw for this example?
A. There is no enough evidence to reject the null hypothesis.
B. We can be 90% confident that the average number of years of education in the U.S. adult population had increased since 2000.
C. The average number of years of education in the U.S. adult population had increased since 2000.
D. There is a significant difference between 2018 and 2000 in terms of the national education level in the U.S. adult population.

Answer 1

Given:

= 13.26, n = 2345, = 13.73, SD(S) = 2.974, = 0.05

24) Null Hypothesis:

Ho: = 13.26

ANSWER: A

A. The average number of years of education in the U.S. adult population did not change much from 2000 to 2018.

25) Alternative Hypothesis:

Ha: > 13.26

ANSWER: C

C. The average number of years of education in the U.S. adult population in 2018 was higher than that in 2000.

26)

ANSWER: D

D. The rejection region is on the right side of the sampling distribution.

27)

Test statistic:

Degree of Freedom = n-1 = 2345 - 1 = 2344

Critical value:

............Using t table

Conclusion:

t < t, n-1, that is 7.65 > 1.646, That is Reject Ho at 5% level of significance

27)

ANSWER: C

C. The average number of years of education in the U.S. adult population had increased since 2000.