{"id":5425,"date":"2022-08-22T21:25:45","date_gmt":"2022-08-22T21:25:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5425"},"modified":"2022-08-22T21:29:04","modified_gmt":"2022-08-22T21:29:04","slug":"12d-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/12d-coreq\/","title":{"raw":"12D Coreq","rendered":"12D Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will be working with intervals\u00a0 as you construct confidence interval estimates of a difference in population means.\r\n\r\nWorking with Intervals that Estimate a Difference\r\n\r\nUsing a cell phone while driving can increase the risk of an accident. One reason for\u00a0 this is that using a cell phone while driving may increase the time it takes to react in\u00a0 various driving situations. But how much does it affect reaction time? To answer a\u00a0 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\u00a0 while driving.\r\n\r\nIn In-Class Activity 10.D, you interpreted confidence intervals that estimated a\u00a0 difference in population proportions. In this corequisite support activity, you will do\u00a0 something similar, but you will be working with intervals for population means rather\u00a0 than proportions.\r\n
\r\n

Question 1<\/h3>\r\n1) 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.\r\n\r\na) In the context of the cell phone reaction time example,\u00a0[latex]\\mu_{cell\\;phone}[\/latex] will represent the mean reaction time of people who use their cell phones while\u00a0 driving. How would you represent the mean reaction time of people who do\u00a0 not use their cell phones while driving?\r\n\r\nb) What does [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] represent?\r\n\r\nc) What would it mean if [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was equal to 0?\r\n\r\nd) What would it mean if [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was greater than 0?\r\n\r\ne) What would it mean if\u00a0[latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was less than 0?\r\n\r\nf) Give an example of an interval of possible values for [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] that would indicate that\u00a0[latex]\\mu_{cell\\;phone}[\/latex] was greater than[latex]\\mu_{no\\;cell\\;phone}[\/latex].\r\n\r\nHint: Would the endpoints of the interval need to be positive or negative?\r\n\r\ng) 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.\u00a0<\/span>\r\n\r\nHint: Would the endpoints of the interval need to be positive or negative?\r\n\r\n<\/div>\r\n ","rendered":"

In the next preview assignment and in the next class, you will be working with intervals\u00a0 as you construct confidence interval estimates of a difference in population means.<\/p>\n

Working with Intervals that Estimate a Difference<\/p>\n

Using a cell phone while driving can increase the risk of an accident. One reason for\u00a0 this is that using a cell phone while driving may increase the time it takes to react in\u00a0 various driving situations. But how much does it affect reaction time? To answer a\u00a0 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\u00a0 while driving.<\/p>\n

In In-Class Activity 10.D, you interpreted confidence intervals that estimated a\u00a0 difference in population proportions. In this corequisite support activity, you will do\u00a0 something similar, but you will be working with intervals for population means rather\u00a0 than proportions.<\/p>\n

\n

Question 1<\/h3>\n

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.<\/p>\n

a) In the context of the cell phone reaction time example,\u00a0[latex]\\mu_{cell\\;phone}[\/latex] will represent the mean reaction time of people who use their cell phones while\u00a0 driving. How would you represent the mean reaction time of people who do\u00a0 not use their cell phones while driving?<\/p>\n

b) What does [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] represent?<\/p>\n

c) What would it mean if [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was equal to 0?<\/p>\n

d) What would it mean if [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was greater than 0?<\/p>\n

e) What would it mean if\u00a0[latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] was less than 0?<\/p>\n

f) Give an example of an interval of possible values for [latex]\\mu_{cell\\;phone}-\\mu_{no\\;cell\\;phone}[\/latex] that would indicate that\u00a0[latex]\\mu_{cell\\;phone}[\/latex] was greater than[latex]\\mu_{no\\;cell\\;phone}[\/latex].<\/p>\n

Hint: Would the endpoints of the interval need to be positive or negative?<\/p>\n

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.\u00a0<\/span><\/p>\n

Hint: Would the endpoints of the interval need to be positive or negative?<\/p>\n<\/div>\n

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