SOLUTIONS ACTIVITY SET 2
Work together to determine answers!
2.1 Car and truck speeds at a particular location have approximately a bell-shaped distribution with mean
= 65 mph and standard deviation = 5 mph.
For parts a-c, use the empirical rule (pp. 53 – 54) or in lecture notes to fill in the blanks in each part:
a. About 68% of cars and trucks travel between ___60____ and ___70____ at this location. Basically for
any bell shaped curve, you will find that roughly 68% of the observations fall within +/- one
standard deviation from the mean. Since the mean here is 65 and s = 5, then 68% of the
observations will fall between 65 +/- 5. Continuing, for 95% this will be the mean +/- 2s and for
99.7% this will be the mean +/- 3s.
b. About 95% of cars and trucks travel between ___55___ and ____75____ at this location.
c. About 99.7% of cars and trucks travel between ___50___ and ____80____ at this location.
d. A z-score (pp. 44 – 45) is a measure of how many standard deviations a value is from the mean. Later
in the course, we will see that it is an important measure of the size of a value.
The formula is Z =
Observed Value - Mean
.
Standard deviation
Determine a z-score for a vehicle speed of 72 mph. Plugging the numbers into the formula:
Z=
72 - 65
= 1.4
5
e. What vehicle speed has a z-score = −1? Said another way, what vehicle speed is one standard deviation
below the mean? (You will need to do some algebra to solve for Observed Value) You need to solve for
the observed value which will produce the following formula:
OV = Mean + SZ, and using this equation to answer the question we plug in:
OV = 65 + (5)*(-1) = 60. So 60 mph would be -1 z-score from the mean.
2.2 Open the Class Survey (Minitab File) data file. The College Board announced that for SAT takers
in 2004 the average results were as follows:
Females: SATM – 501 and SATV – 504
Males:
SATM – 537 and SATV – 512
You are a researcher and want to use our class survey data to research how PSU undergraduate students
compare to these national averages. .
a. Is this an experiment or an observational study? Explain. Using our class survey would be
considered an observational study. This is due to not having used any randomization or
manipulation of treatments in our selection process. If we would have randomly selected the
students from the population of all PSU undergraduate students then we may have considered this
an experimental study.
b. The purpose of most statistical studies is to use the sample data to generalize to a larger group. What do
you think are the weaknesses of this study for generalizing to all PSU undergraduate students? In order
to generalize to a larger group, i.e. all PSU undergraduate students, your sample group needs to be
representative of this larger group. That is, the make up of your sample group should reflect that of
the larger group. For instance, does our class reflect the undergraduates as a whole in regards to
percentage of females and percentage of race? The best way to accomplish this would be through
random sampling.
c. (Importance of checking data). Compute the Descriptive Statistics for SATM (C16) and SATV (C17).
Note the minimum and maximum value for each. (REMEMBER: Stat > Basic Statistics > Display
Descriptive Statistics. Enter together into the Variables window SATM and SATV.)
i.
From the output, what does the * represent? The * represents missing data and the N*
represents the number of missing data points for that variable. That is, 10 students
did not provide and answer to SATM and 11 students did not answer SATV.
ii.
How many students completed the question regarding their SATM and SATV scores?
SATM 216
SATV 215
d. Now find the Descriptive Statistics for SATM and SATV by Gender (Repeat what you did for part c
but now enter Gender in the By Variable window) and use the output to answer the following:
Female SATM: Q1 537.50
Male SATM: Q1 570.00
Female SATV: Q1 530.00
Male SATV: Q1 525.00
Q3 650.00
Q3 670.00
Q3 620.00
Q3 645.00
IQR 112.50
IQR 100.00
IQR 90.00
IQR 120.00
f. Using the 5-number summary, a data point is considered an outlier on a boxplot if it is either larger than
Q3+ (1.5IQR), or smaller than Q1  (1.5IQR).
For Females
SATM: Calculate the value of Q3+ (1.5IQR) = 650 + 168.75 = 818.75
SATM: Calculate the value of Q1  (1.5IQR) = 537.50 – 168.75 = 368.75
SATV: Calculate the value of Q3+ (1.5IQR) = 620 + 135 = 755
SATV: Calculate the value of Q1  (1.5IQR) = 530 – 135 = 395
For Males
SATM: Calculate the value of Q3+ (1.5IQR) = 670 + 150 = 820
SATM: Calculate the value of Q1  (1.5IQR) = 570 – 150 = 420
SATV: Calculate the value of Q3+ (1.5IQR) = 645 + 180 = 825
SATV: Calculate the value of Q1  (1.5IQR = 525 – 180 = 345
g. Use the Descriptive Statistics you calculated by Gender to answer the following:

How do the SAT scores of PSU students compare to the national average? Do you believe that
any differences are significant? That is, do you think these differences are large enough that
statistically they are the different? (Recall that the national averages were: Females: SATM –
501 and SATV – 504; and for Males
SATM – 537 and SATV – 512 ) The SAT scores for
the PSU students is higher than the national averages for both gender and SAT sections.
We will study later this semester how do determine if these differences are statistically
significant or just represent small, but not noteworthy, differences.

How do the SAT scores from our survey compare across gender? Do you believe that any
differences are significant? That is, do you think these differences are large enough that
statistically they are the different? For both the Math and Verbal sections of the SAT, the
males reported higher mean scores. However, since both of the female means are within
the IQR of the males, I doubt if the difference is significant. Again, we will study later
this semester how do determine if these differences are statistically significant or just
represent small, but not noteworthy, differences.