Discussion:
Task:
Suppose your organization is committed to the promotion of public health in Boston, and your department specifically focuses on teenagers. With the permission of several area middle and high schools, your organization fielded a survey to a large group of students. The questionnaire included several health behavior related questions, including whether the student smokes, and if so, what age they started and how many cigarettes/packs per week they typically smoke. For this problem, we will only be looking at a small portion of the data set - specifically the high school seniors from the sample who indicated that they smoke. The data set (attached as an Excel file) includes the age at which these high school students began smoking.
a) Using SPSS, calculate the mean, SD, and SE.
b) Using SPSS, create a histogram for the sample
c) Estimate the population mean using the 95% confidence interval
d) State your conclusion following the format we discussed in class (however, instead of using "population mean" substitute in what the population mean actually represents - in this case "the mean starting age of Boston teenagers who smoke")
e) Assuming that the true population mean (which in this case refers to the starting age of teenage smokers in the Boston area) is 15.5, create a sampling distribution (distribution of the sample means) and mark out 3 standard errors (SE) in each direction. (This can be drawn by hand).
f) Referring to your graph (and considering other possible sample means you could have obtained), explain why you are 95% confident that your confidence interval in part (d) "captures" the true population mean.
g) Is it possible that you could have a sample (no matter how well you designed the study) in which the mean and resulting confidence interval would not include the true population mean? If so, what is the probability of this occurring? Explain.
| ID |
AgeStart |
| 1 |
11 |
| 2 |
12 |
| 3 |
12 |
| 4 |
12 |
| 5 |
13 |
| 6 |
13 |
| 7 |
13 |
| 8 |
13 |
| 9 |
13 |
| 10 |
14 |
| 11 |
14 |
| 12 |
14 |
| 13 |
14 |
| 14 |
14 |
| 15 |
14 |
| 16 |
14 |
| 17 |
14 |
| 18 |
14 |
| 19 |
15 |
| 20 |
15 |
| 21 |
15 |
| 22 |
15 |
| 23 |
15 |
| 24 |
15 |
| 25 |
15 |
| 26 |
15 |
| 27 |
15 |
| 28 |
15 |
| 29 |
15 |
| 30 |
16 |
| 31 |
16 |
| 32 |
16 |
| 33 |
16 |
| 34 |
16 |
| 35 |
16 |
| 36 |
16 |
| 37 |
16 |
| 38 |
17 |
| 39 |
17 |
| 40 |
17 |
| 41 |
17 |
| 42 |
17 |
| 43 |
17 |
| 44 |
17 |
| 45 |
17 |
| 46 |
17 |
| 47 |
17 |
| 48 |
18 |
| 49 |
18 |
| 50 |
18 |