Question

Situation:

A survey was conducted to determine whether a proposed federal law should be passed to over haul the health care system in U.S. The following data was collected recording the number of people favoring the law based on their age group. It is believed that the distribution of the people favoring passing the law varies based on the age of the survey participants.

Action:

Using the chi-square goodness of fit test and either Excel or Minitab, determine whether age varies among survey participant favoring the proposed law. Use a .01 level of significance and the following observed frequencies of survey participants favoring passing the proposed law. Use the hypothesis testing procedure appropriate for this problem to help you make a decision.

Age of Survey Participants		Frequency
Under 20		23
20 to under 30		40
30 to under 40		56
40 to under 50		50
50 to under 60		32
Over 60		29

1. SHOW THE Ho AND Ha APPROPRIATE FOR THIS PROBLEM

2. WHAT IS THE P-VALUE FOR THIS PROBLEM?

3. COMPARE P-VALUE TO PROBLEM STATEMENT SPECFIED SIGNIFICANCE VALUE AND STATE WHETHER Ho SHOULD OR SHOULD NOT BE REJECTED

4. BASED ON WHETHER Ho IS REJECTED/NOT REJECTED, STATE WHETHER THE DISTRIBUTION OF THE SURVEY PARTICIPANTS FAVORING THE PROPOSED LAW VALIES BASED ON THE AGE OF THE PARTICIPANTS.

Answer 1

a)

Null and Alternate Hypothesis

H₀: There is equal distribution for all the age years

H₁: Law varies based on the age

Observed Values

Age of Survey Participants	Under 20	20 to under 30	30 to under 40	40 to under 50	50 to under 60	Over 60	Total
Frequency	23	40	56	50	32	29	230

Degrees of Freedom = 6-1 = 5

Alpha = 0.01

Critical Value = 15.09

Expected Values

For Each Year = 230/6 = 38.3

Test Statistic:

Chi-Square = ∑(O_i-E_i)²/E_i

Chi-Square = (23-38.3)²/38.3 + ……. + (29-38.3)²/38.3 = 21.22

b)

p-value = 0.000736

c)

Results

Since the p-value is less than 0.01, we reject H₀ with at least 99% confidence.

d)

Conclusion

At alpha = 0.01, we are confident that Law varies based on the age