Question

A sample of 449 government employees and some number of respondents from private corporations answered the question about their education in 2018. Compare their average highest year of school completed and answer the question: Did government employees on average have more education than private employees in the U.S. in 2018? Explain why you think so. [Do not run the test in SPSS. Use the SPSS output below.]

T-Test

Group Statistics
	Govt or private employee	N	Mean	Std. Deviation	Std. Error Mean
Highest year of school completed	GOVERNMENT	449	14.85	2.823	.133
	PRIVATE	-------	13.52	2.917	.069

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
Highest year of school completed	Equal variances assumed	.491	.483	8.672	2210	.000	---------	.153	1.028	1.629

1. Calculate the values to put into two blanks (----). [See the output above].

2. State the null hypothesis (in words).

3. State the research (one-tailed) hypothesis (in words). [Hint: inspect the sample means for stating correct direction].

4. Find t_critical for one-tailed test.

5. Based on this SPSS output at the 0.05 significance level do you reject or accept the null hypothesis? Why?

6. Based on this SPSS output at the 0.05 significance level, do you reject or accept the one-tailed research hypothesis?

7. Answer the problem’s question.

Answer 1

1.

First Blank: the value of n for private employee

We know that,

Std. error = Std. Deviation/

i.e. 0.069 = 2.917/

n = 1787.21

~ 1788

Second blank: Mean difference

t = Mean difference/std. error difference

So,

Mean difference = 8.672*0.153

= 1.327

2.

H₀: Government employees and private employees on average have equal education in the U.S. in 2018.

3.

Research Hypothesis: Government employees on average have more education than private employees in the U.S. in 2018

4.

We know that,

df = n1 + n2 - 2

= 449+1788-2

= 2235

= 0.05

So,

t_{critical =} 1.646

6.

Since significance value = 0 < 0.05 i.e. we can reject null hypothesis.

6.

Since t = 8.672 > t_{critical =} 1.646 i.e. we can reject null hypothesis.

7.

We have enough evidence to conclude that government employees on average have more education than private employees in the U.S. in 2018.

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