Answer the question below using hypothesis testing. Follow the seven-step proced

Question

Answer the question below using hypothesis testing. Follow the seven-step procedure
for testing a hypothesis in your text book as a guide for answering the questions. Use a .05
significance level. In each case, calculate the p-value.

3. Did the LFPR increase between 1968 and 1972? Use a pooled t-test.

Women in the Labor Forc Labor Force Participation Rates by city in 1968 City N.Y LA. Chicago Philadelphia Detroit San Francisco Boston Pitt. St. Louis Connecticut Wash., D.C. unn Baltimore Newark Minn/St. Paul Buffalo Houston Patterson Dallas 1972 1968 0.45 0.42 0.50 0.50 0.52 0.52 0.45 0.45 0.46 0.43 0.55 0.55 0.60 0.45 0.49 0.34 0.35 0.45 0.55 0.54 0.52 0.42 0.53 0.51 0.57 0.49 0.53 0.54 0.59 0.50 0.64 0.58 0.50 0.49 0.57 0.56 0.64 0.63

Explanation / Answer

Set Up Hypothesis
Null, no LFPR significance between 1968 and 1972, Ho: u1= u2
Alternative , LFPR increase between 1968 and 1972, H1: u1 < u2
Test Statistic
X (Mean)=0.4932; Standard Deviation (s.d1)=0.068
Number(n1)=19
Y(Mean)=0.5268; Standard Deviation(s.d2)=0.0708
Number(n2)=19
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (18*0.0046 + 18*0.005) / (38- 2 )
S^2 = 0.0048
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=0.4932-0.5268/Sqrt((0.0048( 1 /19+ 1/19 ))
to=-0.0336/0.0225
to=-1.4948
| to | =1.4948
Critical Value
The Value of |t | with (n1+n2-2) i.e 36 d.f is 1.688
We got |to| = 1.4948 & | t | = 1.688
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -1.4948 ) = 0.07184
Hence Value of P0.05 < 0.07184,Here We Do not Reject Ho

We have evidence that no LFPR significance between 1968 and 1972

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