In: Physics
The student union wants to determine the mean number of hours per week a student at Okanagan College studies. To accomplish this, they passed a questionnaire to 14 randomly chosen students among first and second year status. They also wanted insure an equal number of men and women to possibly investigate gender differences. The results were: Year of study 1 2 1 1 2 2 1 1 2 2 2 1 1 2 Mean hours studied per week 4 12 7 10 15 5 2 15 15 21 8 14 9 20 Gender M M M M M M M F F F F F F F
(a) What is the population of interest? (b) What is the sampling frame?(h) Find the 10% trimmed mean for all individuals ? (e) What are the dependent and independent variables if investigating gender differences in mean hours studied per week? (n) Suppose you multiple all the data by 2. What will be the new mean and standard deviation?(s) Draw a clustered bar chart (by gender), using partitions for hours in groups of 0-9, 10-19, and 20+. (t) Can you conclude that there is an association between the mean number of hours per week spent studying and gender? Justify your answer.
For the given data set
Year | Mean hours | Gender |
1 | 4 | M |
2 | 12 | M |
1 | 7 | M |
1 | 10 | M |
2 | 15 | M |
2 | 5 | M |
1 | 2 | M |
1 | 15 | F |
2 | 15 | F |
2 | 21 | F |
2 | 8 | F |
1 | 14 | F |
1 | 9 | F |
2 | 20 | F |
a. The population which is considered for the study or
statistical inference is known as the population of interest in
statistical analysis. It is the population that is
under study and for which the data is collected. In statistics, the
population of interest can be objects, people, measurements
etc.
For the given case, population of interest is a group of 14
students, 7 males and 7 females from 1st and 2nd years of
studies
b. The sample frame is as under
Year | Mean hours | Gender |
1 | 4 | M |
2 | 12 | M |
1 | 7 | M |
1 | 10 | M |
2 | 15 | M |
2 | 5 | M |
1 | 2 | M |
1 | 15 | F |
2 | 15 | F |
2 | 21 | F |
2 | 8 | F |
1 | 14 | F |
1 | 9 | F |
2 | 20 | F |
h. 10% trimmed mean is found using excel function
=TRIMMEAN(B2:B15,10%)
10% trimmed mean is 11.214 hours
e. if studying gender differences in mean hours studied per
week
then independent variable is year of study and gender and the
dependent variable is mean number of hours studied
n. if we multiply all the data points by 2
old mean is 11.21429 hours per week
new mean 22.42857 hours per week
old SD = 5.7808319 hours per week
new SD = 11.14011 hours per week
s. the following is gender based bar graph in clusters
t. we can see from the bar graph mean number of hours studied per
week are higher for females and hence there is a obvious
association