Posted April 23. Due: Tue April 28 for early grading, or Thu April 30.
Remember to always explain your answers.
We plan to poll 200 students enrolled in statistics at your college by distributing surveys during class. Which of the following hypotheses could be tested with the survey results? Mark each as valid (OK to use to test the hypothesis) or not valid (should not be used to test the hypothesis). Of course, explain why valid/invalid!
The hypothesis that p = 0.60, where p is the proportion of students at your college who study the recommended “2 hours a week for each class unit.”
The hypothesis that p = 0.60, where p is the proportion of students at your college who visit a dentist at least once a year.
The hypothesis that p = 0.60, where p is the proportion of students at your college who are receiving some form of financial aid.
The hypothesis that p = 0.60, where p is the proportion of students at your college who spend more than $600 per semester on textbooks.
In each of the following scenarios, you need to decide whether it is appropriate to use the z-test for the population proportion p, and if not, which condition is violated.
Scenario 1: The UCLA Internet Report (February 2003) estimated that roughly 8.7% of Internet users are extremely concerned about credit card fraud when buying online. Has that figure changed since? To test this, a random sample of 100 Internet users was chosen. When interviewed, 10 said that they were extremely worried about credit card fraud when buying online. Let p be the proportion of all Internet users who are concerned about credit card fraud.
Which one of the following statements is correct about using the z-test for p?
Scenario 2: The UCLA Internet Report (February 2003) estimated that a proportion of roughly .75 of Internet-using homes are still using dial-up access, but claimed that the use of dial-up is declining. Is that really the case? To examine this, a follow-up study was conducted a year later in which out of a random sample of 1,308 households that had an Internet connection, 804 were connecting using a dial-up modem. Let p be the proportion of all U.S. Internet-using households that have dial-up access.
Which one of the following statements is correct about using the z-test for p?
We would like to find out the following: Has the proportion of U.S. adults who support the death penalty for convicted murderers changed since 2003, when it was 0.64? We take a random sample of 1000 US adults and learn that 675 are in favor of the death penalty for convicted murderers.
College students at a large state university completed a survey about their academic and personal life. Questions ranged from “How many credits are you registered for this semester?” to “Would you define yourself as a vegetarian?” Four sections of an introductory statistics course were chosen at random from all the sections of introductory statistics courses offered at the university in the semester when the survey was conducted, and the 312 students who completed the survey were students registered in one of the four chosen sections.
In this exercise, we will use a subset of variables from the survey and use the collected data to answer three questions. Note that (1) these are real data, and (2) the symbol * means that this observation is not available (this is known as a “missing value”).
Here are the variables in the data and their meaning:
We will start by answering some questions about the data.
Out of the first ten students in the datafile, how many did better on the verbal portion of the SAT compared to the math portion?
Out of the first ten students in the datafile, how many are at least somewhat vegetarian?
How many hours does the first junior in the datafile who does not own a cell phone spend sleeping in a typical day?
The next step in understanding the problem is addressing the issues of sampling and study design, which have implications on the generalizability of the results and the type of conclusions you can draw from them.
The mean verbal SAT score of all the students in this university is 580. Is this also the case for all stat students at this university? Note that verbal SAT scores in the U.S. have a standard deviation of 111.
Based on a recent study, roughly 80% of college students in the U.S. own a cell phone. Do the data provide evidence that the proportion of students who own cell phones in this university is lower than the national figure?
Adults in the U.S. average 7 hours of sleep a night. Is this also the mean for all stat students at this university?
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