SOLUTION: Last year income (in minimum wages) in city A was well represented by X ~ N (2,5; 4). An economist wants to test whether there was an increase in average income this year, and for

Question 1105390: Last year income (in minimum wages) in city A was well represented by X ~ N (2,5; 4). An economist wants to test whether there was an increase in average income this year, and for that she took AAS of size n = 64.
a) construct a hypothesis test for this situation with α = 0.05 (define a decision rule)
b) Suppose that X (x-bar) = 2.8 was observed. What is the end of the test? Construct a confidence interval (μ, 0.95)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: mean is < = 2.5
Ha: mean is > 2.5 , one-tail test
alpha is 0.05
test statistic is a t=(bar-mean)/s/sqrt(n)
critical value is t>1.683
CI one way test is (-oo, mean+1.683*4/8) or (-oo, 2.8+0.84) or (-oo, 3.64,) for lower interval, and the value of 2.5 is in the interval
Two way tests are easier with CI
Here the t-value is 2.01 (0.975, df=63)
the CI is sample mean +/- 2.01*0.5 or 1.01 (rounded)
(1.79, 3.81) is 95% CI; 2.5 is in the interval, so there is not evidence to support an increase in income.

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