Question 918897: Based on historical information, it is assumed that no more than 35%
of aggregate household income is spent on food. A researcher believes
that this proportion is now lower with increase in real wages. A study of
82 persons show that 37 spend less than 35%, is there reason at the
5% significance level to believe that the proportion is now lower?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Based on historical information, it is assumed that no more than 35%
of aggregate household income is spent on food. A researcher believes
that this proportion is now lower with increase in real wages. A study of
82 persons show that 37 spend less than 35%, is there reason at the
5% significance level to believe that the proportion is now lower?
-------------------
Ho: p >= 0.35
Ha: p < 0.35 (claim)
---------------
p-hat = 37/82 = 0.82
test stat:: z(0.82) = (0.82-0.35)/sqrt[0.35*0.65/82] = 15.56 (that's enormous)
---
p-value = p(z > 15.56) = 0
----
Conclusion:: Since the p-value is less than 5%, reject Ho.
The test results support the claim.
Cheers,
Stan H.
\-------------------
|
|
|
