We can define the two populations as follows:
Population 1: All drivers driving while talking on the phone
Population 2: All drivers driving while not on the phone and have a cell phone
1) What is the data type?
a. Categorical ?
b. Continuous
2) What is the type of the parameter?
a. Average ?
b. V ariability ?
c. Proportion ?
d. None of the above
3) What is the parameter?
a. Average reaction time of a driver ?
b. Difference in variability of reaction time of a driver while on the phone and that of a ?driver while not on the phone ?
c. Difference between average reaction time of a driver while on the phone and that of a ?driver while not on the phone ?
d. The ratio of variances of reaction time of a driver while on the phone and that of a driver ?while not on the phone
4) How the samples were collected?
a. Independent samples ?
b. Matched pairs sample
5) Which of the following describes the "proper" setup of null hypothesis ??0?
a. ??0:??1-??2>0
b. ??0:??1-??2<0
c. ??0:??1-??2=0
d. ??0:????=0
e. ??0:????>0
f. ??0:??1=??2
g. ??0:??1>??2
h. ??0:??1
6) Which of the following describes the "proper" setup of the alternative hypothesis ??1?
a. ??1:??1-??2>0
b. ??1:??1-??2<0
c. ??1:??1-??2=0
d. ??1:????=0
e. ??1:????>0
f. ??1:??1=??2
g. ??1:??1>??2
h. ??1:??1
Now follow the steps to test the above developed hypothesis (as we did in class) and along the way answer the following questions.
7) Which of the following best describes what it means that "the significance level is 3%"? (As a practice for the exam, make sure you know why all the other options than the one you choose are wrong)
a. We would like to have 3% confidence in our results ?
b. There is 3% chance that our hypothesis ?? is not true ?
c. There isn't enough evidence to conclude that drivers talking on cell phones crash more than drivers who don't
d. Any event that happens with likelihood more than 3% is considered probable to happen ?
e. Any event that happens with likelihood less than 3% is considered probable to happen
8) Test the hypothesis you developed above assuming equal variances. What is the p-value?
a. 7.44 ?
b. 0.002 ?
c. 0.03 ?
d. V ery close to 0 ?
9) What does the p-value you obtained in the above question measure? (As a practice for the exam, make sure you know why all the other options than the one you choose are wrong)
a. The likelihood that the assumption ??0 is true ?
b. The likelihood of seeing a statistic value close to 0 ?
c. The likelihood that the statistic we have got in this sample will be true ?
d. The value of the statistic that we call rare ?
e. The likelihood of seeing a statistic value as extreme as what we have got in this sample
10) Which of the following can be concluded at 3% significance level?
a. Typical reaction times are slower for drivers using cell phones ?
b. Typical reaction times are faster for drivers using cell phones ?
c. There is no difference in typical reaction time whether or not a cell phone is used ?
d. Cannot be determined.
In question 8 we assumed the variances to be equal. Now we would like to test and see whether this assumption was true or not. Write down the null and alternative hypothesis for this test then answer the following questions.
11) What is the p-value for testing whether variances are equal or not?
a. 0.03 ?
b. 0.035 ?
c. 0.07 ?
d. 0.73
12) From the p-value above, we can conclude at 3% significance level:
a. The reaction times for drivers using cell phone is more variable than those not using cell ?phone ?
b. The reaction times for drivers using cell phones is less variable than those not using cell ?phones ?
c. The variability of reaction times for drivers using cell phones can be assumed to be the ?same as that for drivers not using cell phones, as we don't have enough evidence to ?conclude otherwise ?
d. The variability of reaction times for drivers using cell phones is not the same as that for ?drivers not using cell phones ?
e. Typical reaction times are slower for drivers using cell phones ?
f. There is no difference in typical reaction time whether or not a cell phone is used.