Question

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
The cell-phone datafile is available in the Data section below.
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. Be sure to number each answer to which
question it answers.
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 pin terms of the variable
Cell.) You do not need to write the notation, you can just write:
o Null:
o Alternate:

Answer 1

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

For this question, the survey that involved comparison was the proportion of US students at the university that owned a smartphone and the proportion of college students in the US that own a smartphone (80%).

Specifically, we want to check if the proportionof smartphone owners at the university is lower than the overall proportion of smartphone owners amongst US college students (80%).

Hence,

The null hypothesis would be that there isn't significant evidence to conclude that the proportion of smartphone owners is lower at this university than the general proportion of smartphone owners amongst college students.

That is, the proportion of smartphone users at this university isn't lower than the proportion of college students in the U.S. that own a smartphone or the proportion of smartphone owners at this university is higher than or equal to the proportion of college students in the U.S. that own a smartphone.

The alternative hypothesis is then that there is significant evidence to conclude that the proportion of smartphone users at this university is lower than the proportion of college students in the U.S. that own a smartphone.

Mathematically,

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Hope this Helps!!!