Question

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Use a level of significance of 0.10.

Northeast      South           West            Central

16.3              16.9              16.4              16.2   

16.1              16.5              16.5              16.6   

16.4              16.4              23.0              16.5   

16.5              16.2              20.2              16.4   

What is the null hypothesis?

What is the alternative hypothesis?

What is test statistic? Please answer with two decimal places.

What is the p-value? Please answer with three decimal places.

What is your conclusion based on the p-value and the level of significance?

What is the proper conclusion?

Answer 1

(a)

H0: Null Hypothesis: (Teenagers obtain their driving licenses at approximately the same average age across the country)

(b)

HA: Alternative Hypothesis: (Teenagers obtain their driving licenses at approximately the different average age across the country) (At least one mean isdifferent from other 3 means)

(c)

From the given values, the following Table is calculated:

Groups	N	Mean	Std. Dev.
Northeast	4	16.325	0.1708
South	4	16.5	0.2944
West	4	19.025	3.1858
Central	4	16.425	0.1708

From the above Table, ANOVA Table is calculated as follows:

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F - Stat	P - Value
Between Groups	3	20.4719	20.4719/3=6.824	F=6.824/2.5736=2.6515	P - Value = 0.0963
Within Groups	12	30.883	30.883/12=2.5736
Total	15	51.3549

The test statistic is given by:

F=6.824/2.5736=2.65

(d)

Degrees of freedom for numerator = 3

Degrees of freedom for denominator = 12

By Technology,

P - Value = 0.096

(e)

Since P - value = 0.096 is less than = 0.01, the difference is ignificant. Reject null hypothesis.

(f)

Proper conclusion:

The data do not support the claim that teenagers obtain their driving licenses at approximately the same average age across the country.