I will post a link to the excel spreadsheet in a dropbox. The following question
ID: 3306488 • Letter: I
Question
I will post a link to the excel spreadsheet in a dropbox. The following questions refer to the excel spreadsheet.
https://www.dropbox.com/s/lqn0j53t16a2ufw/ACT%202%20.xlsx?dl=0
Does the bar chart show a data set to which the Empirical Rule can be applied? Why or why not? (Note that this question is not asking you to apply the Empirical Rule at this time, just whether or not the rule is applicable to this data set.)
Assuming that the Empirical Rule is applicable to this data set, then according to that rule, in what interval of heights would at least 95% of the students lie? What percentage of the students in this sample in fact reported a height within this interval? (Note that this will again require some counting in Excel.)
Which is larger, the standard deviation of the heights of only the female students or the standard deviation of the heights of all students? What does this imply about the two distributions? Why does this make sense? (Make sure that your explanation clearly reflects your understanding of what the standard deviation measures.)
Explanation / Answer
Question
Does the bar chart show a data set to which the Empirical Rule can be applied? Why or why not?
Answer:
Yes, the bar chart shows a data set to which the Empirical Rule can be applied because the given bar chart shows that the given data follows an approximate normal distribution.
Question
Assuming that the Empirical Rule is applicable to this data set, then according to that rule, in what interval of heights would at least 95% of the students lie? What percentage of the students in this sample in fact reported a height within this interval?
Answer:
We know that the empirical rule says that about 95% of the area of distribution will lies between 2 standard deviations from the mean.
We are given
Mean = 67.7867
SD = 4.5727
Lower limit = Mean – 2*SD = 67.7867 – 2*4.5727 = 58.6413
Upper limit = Mean + 2*SD = 67.7867 + 2*4.5727 = 76.9321
At least 95% of the heights of students will lies between 58.64 and 76.93 units.
For the given sample,
Number of observations outside above interval = 25
Total number of observations = 600
Number of observations inside above interval = 600 – 25 = 575
Percentage of students = 575/600 = 0.958333
About 95.83% of the students in the given sample reported a height within above calculated interval.
Question
Which is larger, the standard deviation of the heights of only the female students or the standard deviation of the heights of all students? What does this imply about the two distributions? Why does this make sense?
Answer:
We are given
Standard deviation (All) = 4.57
Standard deviation (Female) = 6.21
The standard deviation for the heights of female students is larger than the standard deviation of the heights of all students.
This implies that there is more variation in the heights of female students as compared to the all students. This makes sense because we observe the variation of heights of female students as compared to all (or only male) students.