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Binge Drinking Among College Students

Binge drinking is defined by the US Department of Health and Human Services as the consumption of five or more drinks in a row for men and four or more for women. In a recent study of 1200 college students, 564 of them reported to have engaged in binge drinking in the past two weeks. The report sought to determine if half of all college students binge drink.

Claim: 50% of college students binge drink.

Null hypothesis:p = 0.50

Alternative hypothesis: p 0.50

Sample size: n = 1200

Population: college students

Distribution: Approximately normal

Please note:

In Chapters 8, 9, and 11 the author describes two types of approaches for deciding whether to reject or not reject the null hypothesis.They are:

• The Critical Value Method
• The P-value Method

For Hypothesis Testing We will use the P-value Method Only!

In this course, we will use the p-value method only.It is the newer of the two methods and is roundly supported by the popular statistics software packages as well as the TI-83 Plus and TI-84 Plus calculators.

Please ignore any Critical Value Method procedures in Chapter's 8, 9, and 11 that appear in your ebook, hardcopy book, or in the author-created videos assigned in this course.Specifically, that means any methods that involve "critical values", "critical regions", or "rejection regions" as part of the hypothesis testing process.

Please respond to allof the questions below.

For each problem:

Show all your work.

Include the name of the software you used, the function, and the inputs to it.

Express any probabilities (p-value) rounded to 3-significant digits.

Explain what your results mean.

1. Complete the hypothesis test about this proportion by performing the following steps. Use a significance level of 0.10.

(a) Calculate the test statistic.

(b) Make a decision to reject or fail to reject the null hypothesis. Use specific wording. Which hypothesis test, in particular, are we rejecting or failing to reject?

(c) Interpret the decision in the context of the original claim. In other words, does the data support the claim that half of all college students binge drink or is there enough evidence to conclude that the proportion of college students who binge drink is different than 0.50?

(d) Is your decision different than that of the students who responded to questions 2 & 3?

2. Complete the hypothesis test about this proportion by performing the following steps. Use a significance level of 0.05.

(a) Calculate the test statistic.

(b) Make a decision to reject or fail to reject the null hypothesis. Use specific wording. Which hypothesis test, in particular, are we rejecting or failing to reject?

(c) Interpret the decision in the context of the original claim. In other words, does the data support the claim that half of all college students binge drink or is there enough evidence to conclude that the proportion of college students who binge drink is different than 0.50?

(d) Is your decision different than that of the students who responded to questions 1 & 3?

3. Complete the hypothesis test about this proportion by performing the following steps. Use a significance level of 0.01.

(a) Calculate the test statistic.

(b) Make a decision to reject or fail to reject the null hypothesis. Use specific wording. Which hypothesis test, in particular, are we rejecting or failing to reject?

(c) Interpret the decision in the context of the original claim. In other words, does the data support the claim that half of all college students binge drink or is there enough evidence to conclude that the proportion of college students who binge drink is different than 0.50?

(d) Is your decision different than that of the students who responded to questions 1 & 2?

4.Construct a 95% confidence interval for the proportion of college students who binge drink (Hint: You will need to look back at chapter 7 to answer this question).

(a) What is the critical value for z for this confidence interval?

(b) Calculate the margin of error?

(c) Determine the confidence interval?

(d) Write a concluding statement (e.g. "I am 95% confident that the proportion of all ..... is between ..... and ......").

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