Question

2. Chi-Square goodness-of-fit test Arn ong the five northwestern states, Washington has 45% of the population, Oregon has 25%, Idaho has 15%, Montana has 10% and North Dakota has 5%. A researcher selects a sample of 100 subjects, with 37 in Washington, 20 in Oregon, 18 in Idaho, 18 in Montana and 7 in North Dakota. Perform the goodness-of-fit test, the claim that the sample of 100 subjects has a distribution that agrees with the distribution of the populations, using a significant level of 0.05.

4

Answer 1

Based on the given data

States	Expected %	Observed Freq (Oi)	Expected ( Ei )
Washington	45%	37	45
Oregon	25%	20	25
Idaho	15%	18	15
Montana	10%	18	10
MNorth Dokata	5%	7	5
Total	100%	100	100

To test

H_o : Sample distribution agrees with distribution of population ( fits good )

H₁ : Sample distribution does not agrees with distribution of population ( does not fit good )

Decision rule is rejest Ho id P - value

Hence P - value < 0.05

=> Reject Ho at alpha = 0.05

Conclusion : ->

There is not sufficent evidence to support claim sample subjects has distribution that agreea with distribution of population at alpha = 0.05.