• Work in groups
• Use the Minitab Worksheet on the disk given out to your group
• Turn in one completed project for your group, with group names

Background.

The university administration has been deeply concerned about the use of marijuana and drinking at the university. To assess the magnitude of the problem suppose a random sample of 222 students at PSU was randomly selected from the 35000 undergraduate students and asked to answer seven questions on a survey form that was given to them:

#1. What is your gender? 0: Male 1: Female
#2. How do you view your weight: 0: Overweight 1: About right 2: Underweight
#3: On the average, how many alcoholic drinks do you have per week? ______
#4: How often have you been pressured to drink? 0: Never 1: Seldom 2: Several times or often
#5: Have you smoked marijuana in the past 6 months? 0: No 1: Yes
#6: Do you think the use of marijuana should be legalized? 0: No 1: Yes
#7: Have you ever ‘binged drink’ (5 or more drinks in one hour)? 0: No 1: Yes

The responses of the 222 students in the sample are contained in the Minitab Worksheet, in the order in which the questions were asked, in Columns 1 through 7, with names reflecting the content of the questions. Treat ‘Gender’ as an explanatory (grouping) variable only. Most of the other 6 items may be either explanatory or response variables depending on what research hypothesis is being examined.

1.  The researcher in charge of the study says that at least half, or 50%, of all the undergraduate students at PSU (i) have smoked marijuana in the past 6 months and (ii) think marijuana should be legalized; and he claims that (iii) at least 75% have binged drank.

1. Give a (point) estimate of the proportion of undergraduate students who have done what the researcher says they have done.

(i) __________ (ii) __________ (iii) ________

2. Obtain 95% confidence intervals for the proportion of all PSU students who have done what the researcher says they have done.

(i) ___________________ (ii) ___________________ (iii) __________________

3. Is the researcher exaggerating the proportions? Or should his assertions be challenged? Specify a null and alternative hypothesis for each of his statements and conduct a test, with the alternative being that the proportions are less than what he says. Use a = .05

i. H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

ii. H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

iii. H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

4. In words, what is a Type I error in the first test above (part i)?

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5. In words, what is a Type II error in the first test above (part i)?

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6. For what values of the sample proportions should the null hypotheses be rejected: values of the sample proportions that are

A. much smaller than ___ B. close to ___ C. much larger than ____ 

the values specified by the null hypothesis?

2.  The researcher also believes that the proportions of males and females who (a) have smoked marijuana in the past 6 months, (b) who believe that marijuana should be legalized and (c) have binged drank, are higher for males than females. Would you agree with him, based on the results of the survey .

9. Give the estimated proportions from the survey for each gender, on each issue:

(a) Males: ____ Females ____

(b) Males: ____ Females ____

(c) Males: ____ Females ____

    ii. Specify null and alternative hypotheses for each of the beliefs (a), (b), and (c). and conduct tests (use a       one-sided alternative in each test)?

(a): H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

(b): H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

(c): H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

3. .The researcher has been led to believe that students consume, on the average, 10 drinks per week and he has told the university’s president that this is true. Should we believe this?

1. Obtain a numerical summary of the number of drinks students consume per week. Give the mean and standard deviation, the 5-number summary, and the IQR.

i. 5-number summary:

ii. Mean (xbar) ______ ii. Standard deviation ______ iii. IQR ______

2. For testing the hypothesis that the average number of drinks per week for all undergraduate students is 10 vs. the alternative that it is not 10, indicate the range of values of xbar for which the null hypothesis should be rejected, that is, what does the rejection region look like?
   
3. The researcher has his assistant conduct the statistical test. Help her out by specifying the null and alternative hypothesis, find the p-value of the test, and tell her what decision she should make:

H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

4. What proportion of students reported not drinking at all? Answer: ________
   
5. What do you think is the appropriate population to use on this issue of the average number of drinks students have per week? (For example, should it be all students at PSU? Or a subset?).
   
6. Irregardless of your answer in (e), investigate whether or not there are significant differences in the average number of drinks by gender, whether or not the student smoked marijuana in the last 6 months, or believes marijuana should be legalized or not (three separate comparisons). Give the average number of drinks/week for each value of the three explanatory (comparison) variables, specify the null and alternative hypotheses you use, give the p-value of the tests, and make your decision.

Gender:

Male Average: ______ Female Average: _______

H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

Smoked marijuana in past 6 months?

Average for ‘No’s’ : ________ Average for ‘Yes’s’: _______

H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

Believe marijuana should be legalized?

Average for ‘No’s’ : ________ Average for ‘Yes’s’: _______

H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ___

4.  Finally, the researcher was interested in knowing if the average number of drinks per week depended on whether or not the students felt they were being pressured to drink or not. Obtain the average number of drinks per week consumed by students who (a) said they were never pressured, (b) seldom pressured, and (c) were pressured several times or often, and test whether or not the differences are statistically significant.

Averages for (a) _________ (b) _________ (c) __________

H₀ : _______ H₁ : _______ P-value: _____ Decision: Reject H₀ ? Yes ___ No ____

 

5.  If you were asked to summarize your results on this subject for the Daily Collegian, what would you say? What did you learn? Anything surprising to you?

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