LAB ACTIVITY 9
Activity 9.1 The term sampling frame refers to the group that actually had a chance to get into the sample. Ideally, this is the same as the population of interest, but sometimes it isn’t. In the following situation, describe the population, the sampling frame, the sample, the parameter of interest, and the statistic.
A Gallup Poll is done using random digit dialing to reach individuals in households with land-line telephones. The purpose is to estimate the proportion of U.S. adults who favor stronger gun control laws. One-thousand persons are sampled, and 63% favor stronger gun control.
a. Population =
b. Sampling frame =
c. Parameter =
d. Sample =
e. Statistic =
Activity 9.2 Access the Class Survey dataset in the Datasets folder of the course web site. Clicking the link will open Minitab.
a. Use Minitab to tally the numbers and percents of students who do and do not smoke cigarettes regularly. (Stat >Tables >Tally) The variable name is Smoke Cigarettes (C10) and are student responses to if they smoke cigarettes.
Smoke Count Percent
No
Yes
b. Use Minitab to determine a 95% confidence interval for the proportion of all PSU students who regularly smoke. (Stat >Basic Statistics >1-proportion, enter Smoke as the variable AND click Options and then check the box to use methods based on the normal curve.)
Write the confidence interval and then write a sentence that interprets the interval.
c. In December 2005, the U.S. Center for Disease Control estimated that 23.6% of Americans between the ages of 18 – 24 smoke cigarettes. Based on the interval computed in part (b), do you think 24% of PSU students smoke cigarettes? Explain.
d. Use Minitab to determine a 90% confidence interval for the proportion of PSU students that smokes cigarettes. (Use the same Minitab method as for part (a) AND click the Options button to access a box where you can change the confidence level to 90.) Write the interval.
e. In general what is the relationship between the confidence level and the width of an interval?
f. Show how to calculate the 90% confidence interval determined in part (d) “by hand.” Use either the lecture notes or in the text.
Activity 9.3 Continue to use the Class Survey data set. The variable named Try Weed(C22) contains responses to a question about whether students have tried marijuana.
a. Use Stat >Tables Cross Tabulation and Chi-square to help you fill in a two-way table for the relationship between the variables Smoke Cigarettes and Try Weed with counts.
Smokes?Weed? / No / Yes / Total
No
Yes
Total
b. Use Minitab to determine a 95% confidence interval for the proportion that tried marijuana in a population of students who smoke. TO DO THIS, again use Stat >Basic Statistics >1-Proportion BUT NOW click on Summarized Data and enter the sample size for number who smoke as “Number of Trials” and enter the number tried marijuana as “Number of events.” You might have to use the Options button to change the confidence back to 95.
What is the sample proportion that tried marijuana for the Smokes group?
What is this 95% confidence interval?
c. Determine separate 95% confidence intervals for the proportion that tried marijuana in a population of students who do not smoke. You can use Minitab.
CI for Do Not Smoke:
d. Use the confidence intervals found for those that smoke (part b) and do not smoke (part c) to make a generalization about the student smoking population with regard to the proportion that tried marijuana.
e. Which of the two intervals is the narrowest (in terms of difference between lower and upper values)? Why do you think this particular interval is the narrower of the two?
f. Show to calculate “by hand” the 95% confidence interval found in part (b) for the smokers.
Activity 9.4 To get a better understanding of the Central Limit Theorem as discussed in the lecture notes you can visit and review a simulation program a (this program is also the one in the lecture notest:
http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html