STA 215 Practice Midterm Exam
1) [25 points] Suppose that the average number of years to graduate at a university is 4 years, with a standard
deviation of 0.5 years. Assume a bell-shaped distribution for years to graduate.
a) From the Empirical Rule, what is a range of values that 95% of the students should graduate between?
b) From the Empirical Rule, what is a range of values that 68% of the students should graduate between?
c) From the Empirical Rule, what is a range of values that 99.7% of the students should graduate between?
d) Suppose that the average height for college men is 66 inches. If the height distribution is bell-shaped, and 95%
of the men have heights between 60 inches and 72 inches, what is the standard deviation of heights for this
population?
e) What is a standardized score (z-score) for 5 years.
2) [20 points] For each relationship (conclusions from one or more studies), define what the response and
explanatory variables are and state whether each variable is categorical or quantitative.
a) Children who take the time to eat breakfast get higher grades in school than children who don’t eat breakfast.
b) The oldest child in a family is more likely to favor the death penalty than the middle or youngest child.
c) Second hand smoke (passive smoke) is a risk factor for chronic lung disease.
d) Listening to Mozart raised non-verbal IQ scores an average of 8 to 9 points higher than listening to relaxation
tapes.
3) [20 points] A regression was done for 20 cities with latitude as the explanatory variable (x) and average January
temperature as the response variable (y). The latitude is measured in degrees and average January temperature in
degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth). The regression equation is
ŷ = 49.4 – 0.313 x
a) Does this equation indicate a positive or negative relationship? Write a sentence exactly interpreting the slope.
b) The city of Miami, Florida has latitude 26 degrees with average January temperature of 67 degrees Fahrenheit.
What is the estimated average January temperature for Miami, based on the regression equation? What is the
residual?
c) The total sum of squares (SSTO) = 4436.6, and the error sum of squares (SSE) = 1185.8. Does this indicate a
strong relationship between latitude and temperature? Explain.
d) Mexico City has latitude 20 degrees. What is the problem with using the regression equation to estimate the
average January temperature for Mexico City?
4) [10 points] Ellen is taking 4 courses for the semester. She believes that the probability distribution function for
X, the number of courses for which she will get an A grade is given below.
k = no. of A’s
P(X = k)
0
0.10
1
0.30
2
0.40
a) What is the probability that Ellen will get 2 or more A’s?
b) What is the value of the cumulative probability distribution at 3, i.e. P(X
3
0.15
4
0.05
 3)?
5) [15 points] In a pond with a large population of turtles, the percent of three different types are
Type of Turtle
Chicken Turtle
Spotted Turtle
Snapping Turtle
Percentage
30%
50%
20%
A random sample of 100 turtles is taken from the pond.
a) What is the standard deviation for the sample proportion, p̂ , of chicken turtles?
b) What is the standard deviation for the sample proportion, p̂ , of spotted turtles?
c)
What is the standard deviation for the sample proportion, p̂ , of snapping turtles?
6) [10 points] Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally
distributed with an average speed = 65 mph and standard deviation = 5 mph.
a) What is the standard deviation for the sample mean speed in a random sample of n = 10 cars?
b) What is the standard deviation for the sample mean speed in a random sample of n = 100 cars?
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