Answer:
(1) Null Hypothesis, 
: 
Alternate Hypothesis, 
: 
(2) Test statistics = -1.48
(3) At the 0.05 significance level, Fair field conclude that the population means are same.
Step-by-step explanation:
Let 
= mean annual family income for 12 people making inquiries at the first development
= mean annual family income for 24 people making inquiries at the second development
= standard deviation of annual family income for 12 people making inquiries at the first development
= standard deviation of annual family income for 24 people making inquiries at the second development
= sample of people of first development i.e. 12
= sample of people of second development i.e. 24
(1) Null Hypothesis, : {population means are same}
Alternate Hypothesis, : {population means are different}
<u>DECISION RULE ;</u>
- If the test statistics is less than the critical value of t from table at 5% significance level, then we will accept null hypothesis, .
- If the test statistics is more than the critical value of t from table at 5% significance level, then we will reject null hypothesis, .
(2) The test statistics is given by;
~ 
where, 
= Sample mean income of people at first development
= $153,000
= Sample mean income of people at second development = $171,000
= $42,000 and = $30,000
= 
= 34344.30
Test statistics = 
~ 
= -1.48
(3) At 5% level of significance, t table gives critical value of 2.032 at 34 degree of freedom.Since our test statistics is less than the critical value of t so considering our decision rule, we will accept null hypothesis.
And conclude that population means are same.
