Question

A researcher is interested in whether salaries for middle school teachers were less than salaries for nurses in Arkansas. A statewide salary survey is conducted using random sampling.

The Data Analysis output for the various tests used when comparing two group means are shown below. The significance level was .05.

F-Test Two-Sample for Variances
	Teachers	Nurses
Mean	45946.07	53365.13
Variance	68256753	86820446
Observations	300	300
df	299	299
F	0.7862
P(F<=f) one-tail	0.0190
F Critical one-tail	0.8265

t-Test: Paired Two Sample for Means
	Variable 1	Variable 2
Mean	45946.07	53365.13
Variance	68256753	86820446
Observations	300	300
Pearson Correlation	0.191488
Hypothesized Mean Difference	0
df	299
t Stat	-11.4663
P(T<=t) one-tail	9.01E-26
t Critical one-tail	1.649966
P(T<=t) two-tail	1.8E-25
t Critical two-tail	1.96793

t-Test: Two-Sample Assuming Equal Variances
	Teachers	Nurses
Mean	45946.07	53365.13
Variance	68256753	86820446
Observations	300	300
Pooled Variance	77538599
Hypothesized Mean Difference	0
df	598
t Stat	-10.319
P(T<=t) one-tail	2.19E-23
t Critical one-tail	1.647406
P(T<=t) two-tail	4.37E-23
t Critical two-tail	1.963939

t-Test: Two-Sample Assuming Unequal Variances
	Teachers	Nurses
Mean	45946.07	53365.13
Variance	68256753	86820446
Observations	300	300
Hypothesized Mean Difference	0
df	590
t Stat	-10.319
P(T<=t) one-tail	2.3E-23
t Critical one-tail	1.64744
P(T<=t) two-tail	4.61E-23
t Critical two-tail	1.963993

a) What is the appropriate two sample test to perform – the paired t test, the t test assuming equal variances, or the t test assuming unequal variances – for this research project?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc).

f) Do you reject or not reject Ho? Explain your decision.

Answer 1

For, Comparing two group means

a)

ANSWER: d

d. t test assuming unequal variances

b)

Let, 1 be the Mean salaries for middle school teachers

2 be the Mean salaries for nurses in Arkansas

Hypothesis:

C)

Decision Rule:

Test statistic < Critical value, then Reject Ho at 5% level of significance.

-10.319 < -1.647, That is Reject Ho at 5% level of significance.

d)

Decision Rule:

P-value < , Then Reject Ho at % level of significance.

Therefore,

P-value < , i.e. 0.000 < 0.05, That is Reject Ho at 5% level of significance.

e)

Test statistic = -10.319

f)

Reject Ho.

Therefore, Salaries for middle school teachers were less than salaries for nurses in Arkansas.