| Stat 251: Statistical Methods I | Last updated 09/25/2008 |
Complete the following exercises from your text: pages 161-166, #4, 10, 12, 21, 22, 26, 27,a,b, 29. Note - there is a typo in the text in number 29. See below for correction.
These exercises are reproduced below.
#4) A tennis fan (that would be Dr. Rossman) recorded data on a random sample of 16 first-round men's singles matches from the 2004 U.S. Open and also on a random sample of 16 first-round women's matches. (The fan did not want to invest the time required to gather and record the data for all matches played in the tournament.) Variables recorded include gender, number of sets played, number of games played, number of points played, and length of match in minutes.
(a) Classify each of these variables as categorical or quantitative.
The sorted data for the number of points played in a match are given here:
Men
55
173
184
206
208
211
223
225
230
234
234
260
261
276
278
296
Women
88
89
95
96
98
107
118
132
140
157
159
171
179
179
183
228
(b) Determine (by hand) the five-number summary for each gender's distribution of the number of points played by each gender.
(c) Conduct an outlier test (page 108) for each gender.
(d) Construct a boxplot for each gender's distribution, placing them on the same scale. (Use Minitab.) (Remember to label your axes and include scales.)
(e) Comment on what the numerical and graphical summaries reveal about the distribution of points between the two genders.
(f) Did all of the men's matches play more points than all of the women's matches? Do men tend to play more points in their matches than women? Explain the difference in these two questions as you justify your answers.
#10) The dotplots on page 161 display the distribution of sleeping times (per day, in hours) of 3 college students (Amber, Katherine, Sarah) for a 9-week period in the fall of 2004.
(a) One of these students developed mononucleosis during the term and so was told to get as much rest as possible for several weeks. Which student do you think this is? Explain your reasoning.
(b) One of these students is the mother of two small children. Which student do you think this is? Explain your reasoning.
(c) Which student recorded her sleeping times only to the nearest hour? Explain.
(d) Which student generally got the most sleep? Which generally got the least?
(e) For one of these students, her mean sleeping time exceeded her median sleeping time. Which student do you think this is? Explain your reasoning.
#12) Reconsider the students' sleeping times from exercise 10. (SleepStudents.mtw)
(a)
Calculate the mean and standard deviation of sleeping times for each student. (Hint:Use Minitab.) (b) For each student, determine the proportion of the 63 sleeping times that fall within 1 standard deviation of the mean. (Hint:Use Minitab.)(c) For which student does the Empirical Rule appear to hold most closely For that student, determine the proportion of sleeping times that fall within 2 standard deviations of the mean.
(d) Suppose that Katherine gets 10 hours of sleep in a particular night. How many hours more than her mean is this? Also calculate the z-score for this value.
(e) Suppose Amber gets 13 hours of sleep in a particular night. How many hours more than her mean is this? Also calculate the z-score for this value.
(f) Which of these (10 hours for Katherine or 13 for Amber) is higher above that student's mean? Which has the higher z-score? Explain why your answers are not the same.
#21) The midrange of a data set is defined to be the sum of the minimum and maximum values divided by 2. The midhinge of a data set is defined to be the sum of the first and third quartiles divided by 2.
(a) Is the midrange a measure of center or a measure of spread? Explain.
(b) Is the midhinge a measure of center or a measure of spread? Explain.
(c) Is the midrange resistant to outliers? Explain.
(d) Is the midhinge resistant to outliers? Explain.
#22)
Reconsider the quiz scores for class B from Investigation 2.1.4 on pages
119-20. Suppose we were to give every student 5 bonus points. (a) How would the mean change? The median? (b) How would the standard deviation change? The interquartile
range? Note: you should explain your answers to (a) and (b) without
carrying out the calculations to find the new values!
#26) Is it possible for an individual to move from one city to another and have the mean IQ decrease in both cities? If not, explain why not. If so, explain what conditions would be needed to make this happen.
#27) Suppose that you record the number of children in each of ten families (labeled as A-J) to be:
|
Family |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
|
Number of children |
1 |
2 |
1 |
0 |
2 |
2 |
3 |
7 |
4 |
2 |
(a) Determine the average (mean) number of children per family.
Now consider the 24 children in these families as the observational units, and consider the variable “number of siblings.” Thus, the one child in family A has 0 siblings, each of the two children in family B has 1 sibling, and so on.
(b) Determine the average number of siblings per child.
#29) Suppose that the body mass index (BMI) of health American males follows a symmetric, mound-shaped distribution with mean 24.5 and standard deviation 3.0 and that the BMI of healthy American females follows a symmetric, mound-shaped distribution with mean 22.5 and standard deviation 3.0.
(a) Between what two values would approximately 95% of the males' BMI values fall?
(b) About what percentage of male BMI values fall below 21.5?
(c) About what percentage of male BMI values fall above 30.5?
(d) About what percentage of female BMI values between 19.5 and 25.5?
(e) About what percentage of female BMI values fall between 16.5 and 28.5? Note - this is a typo in the text.
(f) Below what value do about 2.5% of female BMI values fall?