18.38 (EX) Student drinking 1/5: A professor asked her sophomore students, “How
ID: 3310033 • Letter: 1
Question
18.38 (EX) Student drinking 1/5: A professor asked her sophomore students, “How many drinks do you typically have per session?” (A drink is defined as one 12 oz beer, one 4 oz glass of wine, or one 1 oz shot of liquor.) Some of the students didn’t drink. Table 18.3 gives the responses of the female and male students who did drink. It is likely that some of the students exaggerated a bit. The sample is all students in one large sophomore-level class. The class is popular, so we are tentatively willing to regard its members as an SRS of sophomore students at this college.
F
3
F
7
F
4
F
4
F
6.5
F
4
F
3
F
6
F
5
F
3
F
8
F
6
F
6
F
3
F
6
F
8
F
3
F
4
F
7
F
4
F
5
F
3.5
F
4
F
2
F
1
F
5
F
5
F
3
F
3
F
6
F
4
F
2
F
7
F
7
F
7
F
5.5
F
3
F
2.5
F
10
F
5
F
4
F
9
F
8
F
1
F
6
F
2
F
5
F
2.5
F
3
F
4.5
F
9
F
5
F
4
F
4
F
3
F
4
F
6
F
7
F
4
F
5
F
1
F
5
F
3
F
4
F
10
F
7
F
3
F
4
F
4
F
4
F
4
F
2
F
1
F
2.5
F
2.5
M
7
M
7.5
M
8
M
15
M
3
M
4
M
1
M
5
M
11
M
4.5
M
6
M
4
M
10
M
16
M
4
M
8
M
5
M
9
M
7
M
7
M
3
M
5
M
6.5
M
1
M
12
M
4
M
6
M
8
M
8
M
4.5
M
10.5
M
8
M
6
M
10
M
1
M
9
M
8
M
7
M
8
M
15
M
3
M
10
M
7
M
4
M
6
M
5
M
2
M
10
M
7
M
9
M
5
M
8
M
7
M
3
M
7
M
6
M
4
M
5
M
2
M
5
M
5.5
M
9
M
10
M
10
M
4
M
8
M
4
M
2
M
4
M
12.5
M
3
M
15
M
2
M
6
M
3
M
4
M
3
M
10
M
6
M
4.5
M
5
a) What is the drinking behavior claimed by sophomore women. Find 95% confidence interval.
b) 18.38 (EX) Student drinking 2/5: What is the drinking behavior claimed by sophomore men. Find 95% confidence interval.
c) 18.38 (EX) Student drinking 3/5: A comparison of the behavior of women and men. Are mean numbers of drinks of women and men different? Let 1 and 2 be the mean numbers of drinks by sophomore women and men. State the hypotheses.
d) 18.38 (EX) Student drinking 4/5: A comparison of the behavior of women and men. Are mean numbers of drinks of women and men different?Carry out the test.
e) 18.38 (EX) Student drinking 5/5: True or False
So we have strong evidence against the null and the mean numbers of drinks are different.
F
3
F
7
F
4
F
4
F
6.5
F
4
F
3
F
6
F
5
F
3
F
8
F
6
F
6
F
3
F
6
F
8
F
3
F
4
F
7
F
4
F
5
F
3.5
F
4
F
2
F
1
F
5
F
5
F
3
F
3
F
6
F
4
F
2
F
7
F
7
F
7
F
5.5
F
3
F
2.5
F
10
F
5
F
4
F
9
F
8
F
1
F
6
F
2
F
5
F
2.5
F
3
F
4.5
F
9
F
5
F
4
F
4
F
3
F
4
F
6
F
7
F
4
F
5
F
1
F
5
F
3
F
4
F
10
F
7
F
3
F
4
F
4
F
4
F
4
F
2
F
1
F
2.5
F
2.5
M
7
M
7.5
M
8
M
15
M
3
M
4
M
1
M
5
M
11
M
4.5
M
6
M
4
M
10
M
16
M
4
M
8
M
5
M
9
M
7
M
7
M
3
M
5
M
6.5
M
1
M
12
M
4
M
6
M
8
M
8
M
4.5
M
10.5
M
8
M
6
M
10
M
1
M
9
M
8
M
7
M
8
M
15
M
3
M
10
M
7
M
4
M
6
M
5
M
2
M
10
M
7
M
9
M
5
M
8
M
7
M
3
M
7
M
6
M
4
M
5
M
2
M
5
M
5.5
M
9
M
10
M
10
M
4
M
8
M
4
M
2
M
4
M
12.5
M
3
M
15
M
2
M
6
M
3
M
4
M
3
M
10
M
6
M
4.5
M
5
Explanation / Answer
(a)What is the drinking behavior claimed by sophomore women. Find 95% confidence interval.
Here sample mean for sophomore women xwomen = 4.5867
sample standard deviation s = 2.10
sample size n = 75
95% confidence interval = xwomen +- tdf, 0.05 (s/n)
= 4.5867 +- 1.99254 * (2.10/ 75)
= 4.5867 +- 0.4832
= (4.1036, 5.0697)
so, on an average a sophore women has 95% probability that they will drink 4.1036 oz to 5.0697 oz.
(b) What is the drinking behavior claimed by sophomore men. Find 95% confidence interval.
Here sample mean for sophomore women xmen = 6.473
sample standard deviation s = 3.4368
sample size n = 93
95% confidence interval = xmen +- tdf, 0.05 (s/n)
= 6.473 +- 1.9861 * (3.4368/ 93)
= 6.473 +- 0.7078
= (5.765, 7.181)
so, on an average a sophore men has 95% probability that they will drink 5.765 oz to 7.181 oz.
(c) H0 : women = men
Ha : women men
(d) Here pooled standard deviation sp = sqrt [{(n1 -1)s12 + (n2 -1)s22}/ (n1 + n2 -2)]
sp = sqrt [{74 * 4.4079 + 92 * 11.8118}/ (74 + 92)] = 2.9174
Test statistic
t = (xmen - xwomen)/ [sp * (1/n1 + 1/n2)] = (6.4731 - 4.5867)/[2.9174 * sqrt(1/75 + 1/93)]
t = 1.8864/ 0.4528 = 4.166
so here critical value of t for alpha = 0.05, dF = 166
t0.05,166 = 1.9744
so here t > tcritical so we shall reject the null hypothesis. mean numbers of drinks of women and men are different.
(e) So we have strong evidence against the null and the mean numbers of drinks are different. that's true.
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