Download Statistics 200 Honors, Fall 2002

Statistics 200 Honors, Fall 2002
Lab assignment #12, Nov. 22
Your Names:
Type or copy/paste your answers to the following questions. Do not erase the questions.
When you finish, print this document and hand it in.
1. Suppose that the heights of 25-year-old males are approximately normally distributed
with mean 71 inches and standard deviation 2.5 inches.
(a) How tall are the tallest 2.5% of males?
(b) What is the probability that a male selected at random is shorter than 68 inches?
2. Data on 224 students who started as computer science majors at a particular university
are collected. Their math SAT scores are analyzed to determine whether high school
males score higher than high school females on the math SAT in the United States.
Relevant Minitab output is shown below.
gender
Female
Male
N
79
145
Mean
565.0
611.8
StDev
82.9
84.0
SE Mean
???
???
95% CI for mu (Female) - mu (Male ): ( -69.8, -23.7)
T-Test mu (Female) = mu (Male ) (vs <): T = ????? P = 0.0000
DF = 162
(a) Find the values of SE Mean for the female and male samples.
(b) Calculate the value of the appropriate t-statistic. Show your work. Do not assume
equal variances.
(c) Although the p-value for the test is very small, we may still have doubts as to
whether high school males score higher than high school females on the math SAT in the
United States. Explain the reason for these doubts.
3. A recent study of college students at a large public university was carried out to
determine whether a student's choice of major has anything to do with whether that
student receives a student loan to pay for a portion of his or her education. Here are the
results from a SRS of 583 students:
Rows: Field of Study
Engish
Columns: Student Loan
no
yes
58.30
41.70
All
100.00
137
98
235
Liberal arts and education
58.22
124
41.78
89
100.00
213
Management
68.00
51
32.00
24
100.00
75
Science
48.33
29
51.67
31
100.00
60
All
58.49
341
41.51
242
100.00
583
Chi-Square = 5.353, DF = ????, P-Value = ?????
Cell Contents -% of Row
Observed Count
(a) Circle every one of the eight cells for which the observed count is higher than the
expected count. Explain your reasoning.
(b) How many degrees of freedom should be used here? Find the p-value for the chisquare statistic of 5.353.
4. Suppose that the heights of 25-year-old women are approximately normally
distributed with unknown mean and unknown standard deviation. We draw a SRS from
the population of 25-year-old women with n=10. We wish to test the null hypothesis H0:
=66 against the one-sided alternative H1: <66.
(a) If we observe the sample standard deviation, s, to be 2.4 inches, what is the standard
error of the sample mean, x-bar?
(b) If we observe the sample mean to be 64, find the t-statistic and the p-value of the test.