In the next preview assignment and in the next class, you will be working with intervals as you construct confidence interval estimates of a difference in population means.
Working with Intervals that Estimate a Difference
Using a cell phone while driving can increase the risk of an accident. One reason for this is that using a cell phone while driving may increase the time it takes to react in various driving situations. But how much does it affect reaction time? To answer a question like this, we could estimate the difference in mean reaction times for people who use their cell phones while driving and people who do not use their cell phones while driving.
In In-Class Activity 10.D, you interpreted confidence intervals that estimated a difference in population proportions. In this corequisite support activity, you will do something similar, but you will be working with intervals for population means rather than proportions.
Question 1
1) In the previous lessons, we used [latex]\mu[/latex] to represent a population mean and [latex]\bar{x}[/latex] to represent a sample mean. When we are comparing two populations, we add subscripts to indicate which population (and sample) is being referenced.
a) In the context of the cell phone reaction time example, [latex]\mu_{cell\;phone}[/latex] will represent the mean reaction time of people who use their cell phones while driving. How would you represent the mean reaction time of people who do not use their cell phones while driving?
b) What does [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] represent?
c) What would it mean if [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] was equal to 0?
d) What would it mean if [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] was greater than 0?
e) What would it mean if [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] was less than 0?
f) Give an example of an interval of possible values for [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] that would indicate that [latex]\mu_{cell\;phone}[/latex] was greater than[latex]\mu_{no\;cell\;phone}[/latex].
Hint: Would the endpoints of the interval need to be positive or negative?
g) Give an example of an interval of possible values for [latex]\mu_{cell\;phone}-\mu_{no\;cell\;phone}[/latex] that would indicate that 0 was a possible value.
Hint: Would the endpoints of the interval need to be positive or negative?
