Question

In: Math

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the...

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 test are you going to run?

One mean t-test

One mean z-test

Chi-Square Goodness of Fit

ANOVA

Question 2

What is the null hypothesis?

Question 2 options:

The mean ages for teenagers obtaining their drivers licenses are approximately the same average age across the country.

At least one of the mean ages for teenagers obtaining their drivers licenses is different from the average age across the country.

Question 3

What is the alternative hypothesis?

Question 3 options:

At least one of the mean ages for teenagers obtaining their drivers licenses is different from the average age across the country.

The mean ages for teenagers obtaining their drivers licenses are approximately the same average age across the country.

Question 4

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

Question 5

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

Question 6

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

Question 6 options:

Reject the null hypothesis

Fail to reject the null hypothesis

Question 7

What is the proper conclusion?

Question 7 options:

At the 0.10 level of significance, the mean ages for teenagers obtaining their drivers licenses are approximately the same average age across the country.

At the 0.10 level of significance, at least one of the mean ages for teenagers obtaining their drivers licenses is different from the average age across the country.

Solutions

Expert Solution

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Northeast 4 65.3 16.325 0.029167
South 4 66 16.5 0.086667
west 4 76.1 19.025 10.14917
Central 4 65.7 16.425 0.029167
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 20.47188 3 6.823958 2.651583 0.096282 2.605525
Within Groups 30.8825 12 2.573542
Total 51.35438 15

Question 1

Answer : ANOVA

Question 2

Answer : The mean ages for teenagers obtaining their drivers licenses are approximately the same average age across the country.

Question 3

Answer : At least one of the mean ages for teenagers obtaining their drivers licenses is different from the average age across the country.

Question 4

Answer : test statistic = 2.65

Question 5

Answer : p-value = 0.096

Question 6

Answer : Reject the null hypothesis

Question 7

Answer :

At the 0.10 level of significance, at least one of the mean ages for teenagers obtaining their drivers licenses is different from the average age across the country.

milcah answered 9 months ago
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