Question

i). Ford says that they expect that 20% of the Mustangs they sell to be Black, 30% Gray & 50% red.    
Conduct a χ2 test to determine if these observed frequencies match Ford's expectation at a 90% LC.


ii).    A sample of 12 NY mob bosses reveals that they paid an average of $1600 in income taxes with σ = $100, while a sample of 10 PA mob bosses paid an average of $1700 with σ = $150. Is the variation here really different @ Fα = 2.0?

iii). [retro] What does the sampling distribution of the sample means allow us to do?


iv)    Give a real world example of a relevant use of an ANOVA F test.


v). Which planet is closer to the Sun:
a.    Earth d.     Pluto
b.    Mars e.     Venus
c.    Jupiter f.      Satern

Answer 1

1. Colour	Observed Frequency	Expected Frequency
   Black	20	33.3	-13.3	176.89
   Gray	30	33.3	-3.3	10.89
   Red	50	33.3	16.7	278.89

   From the given data , expected Frequency = =

We are asked to test whether Ford's observed frequencies matches thier expected frequencies at 90% L.C.

Our null and alternative hypotheses are :

Our test statistic is:

Putting values we get

Here tabulated value of at   at 2 d.f.

Since tabulated avlue of chi square is less than calculated value, we reject our null hypothesis and conclude that observed frequency doesn't equals expected frequency at 90% L.C.

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