Mathematics Homework Help

Variables

• Math: Math SAT score
• Verbal: Verbal SAT score
• Credits: Number of credits the student is registered for
• Year: Year in college (1=Freshman, 2=Sophomore, 3=Junior, 4=Senior)
• Exercise: Time (in minutes) spent exercising in a typical day
• Sleep: Time (in hours) spent sleeping in a typical day
• Veg: Are you a vegetarian (yes, no, some)
• Cell: Do you own a smart phone (yes, no)

Data

If you have not done so already, open the cell-phones datafile in the Stats at Cuyamaca College group on StatCrunch (directions – opens in a new tab).

Context

In 2015 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?”

The researcher randomly selected 325 students from the university; 312 responded to the survey.

Prompt

Once again, here is the research question for this lab.

Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university?

Respond to each of the following in your initial post.

1. State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.)
2. StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met.
3. Use StatCrunch to conduct the hypothesis test. (directions)
   Copy and paste the results (the StatCrunch output window) into the textbox.
4. Give your P-value and interpret its meaning as a conditional probability.
5. State a conclusion that answers the research question. Use a significance level of 5%. (Be sure to state your conclusion in context. This means you should include the P-value, and reference the population and the variable Cell in your conclusion.)

We cannot know whether a Type 1 or Type 2 error actually occurs in a hypothesis test. But, based on the results of our hypothesis test, we should be aware of which type of error is possible and what that error means in the context of our test.

1. For the hypothesis test you conducted above, which type of error is possible, Type 1 or Type 2? Briefly explain why.
2. In the context of your hypothesis test, describe a potential consequence of this type of error.