91Ó°ÊÓ

Suppose a group is interested in determining whether teenagers obtain their driver's 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 driver's licenses.

$\begin{array}{|llllll|}\hline & \text{Northeast}& \text{South}& \text{West}& \text{Central}& \text{East}\\ & 16.3& 16.9& 16.4& 16.2& 17.1\\ & 16.1& 16.5& 16.5& 16.6& 17.2\\ & 16.4& 16.4& 16.6& 16.5& 16.6\\ & 16.5& 16.2& 16.1& 16.4& 16.8\\ \stackrel{¯}{x}=& & & & & \\ s^2=& & & & & \\ \hline\end{array}$

$\mathrm{Î\pm }=0.05$

a) Decision: _____

b) Conclusion: _____

Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for $20$commutes. The first worker’s times have a variance of $12.1$. These coworkers' times have a variance of $16.9$. The first worker thinks that he is more consistent with his commute times. Test the claim at the $10$% level. Assume that commute times are normally distributed. What is s_$2$ in this problem?

Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for $20$commutes. The first worker’s times have a variance of $12.1$. These coworkers' times have a variance of $16.9$. The first worker thinks that he is more consistent with his commute times. Test the claim at the $10$% level. Assume that commute times are normally distributed. What is the p-value?

Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are more consistent.

What is the p-value?

Three different traffic routes are tested for mean driving time. The entries in the Table 13.18 are the driving times in minutes on the three different routes.

State${\mathrm{SS}}_{\text{between}},{\mathrm{SS}}_{\text{within}},$and the $F$statistic.

There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test.

State the null hypothesis for a one-way ANOVA test if there are four groups.

60. 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.

State the hypotheses.
$H_0:-----$
$H_a:-----$

13.2 The F Distribution and the F-Ratio
Use the following information to answer the next three exercises. 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.

$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2={\mathrm{μ}}_3={\mathrm{μ}}_4={\mathrm{μ}}_5$
$H\mathrm{Î\pm }$: At least any two of the group means ${\mathrm{μ}}_1,{\mathrm{μ}}_2,…,{\mathrm{μ}}_5$ are not equal.

61. degrees of freedom $-$ numerator: $df(num)=$

64. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of $10\%$, test the hypothesis that the three formulas produce the same mean weight gain

A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed $24$individuals and asked them their daily one-way commuting mileage. The results are in Table 13.22. Using a $5\%$significance level, test the hypothesis that the three mean commuting mileages are the same.