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.
FTest TwoSample for Variances 

Teachers 
Nurses 

Mean 
45946.07 
53365.13 
Variance 
68256753 
86820446 
Observations 
300 
300 
df 
299 
299 
F 
0.7862 

P(F<=f) onetail 
0.0190 

F Critical onetail 
0.8265 
tTest: 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) onetail 
9.01E26 

t Critical onetail 
1.649966 

P(T<=t) twotail 
1.8E25 

t Critical twotail 
1.96793 
tTest: TwoSample 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) onetail 
2.19E23 

t Critical onetail 
1.647406 

P(T<=t) twotail 
4.37E23 

t Critical twotail 
1.963939 
tTest: TwoSample 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) onetail 
2.3E23 

t Critical onetail 
1.64744 

P(T<=t) twotail 
4.61E23 

t Critical twotail 
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 H_{0} 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.
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:
Pvalue < , Then Reject Ho at % level of significance.
Therefore,
Pvalue < , 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.
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