STA 205
FINAL EXAMINATION
SPRING 2009
NAME ___________________________________________________
INSTRUCTIONS
1. Show ALL WORK TO BE GRADED ON THIS TEST PAPER to receive ANY CREDIT.
2. You may use a formula sheet, a calculator, and the tables attached.
3. Points are in parentheses.
1. A. The wing-lengths of one species of cicada have a mean of 16 mm and a standard deviation of 2.1
mm. If the wing-lengths are normally distributed, what proportion of these cicadas have wing-lengths
less than 17 mm? (10)
B. Find a wing-lengths, W, such that 95% of all of these cicadas have wing-lengths more than W. (10)
C. A random sample of 50 of these cicadas is selected: what is the probability that the sample mean
wing-length x will be less than 17 mm? (12)
2. Brews at the ball game are supposed to average 16 ounces. A fan takes a random sample of 40 cups
(over forty games – drinking responsibly, of course) and finds a mean fill of 15.5 ounces. It is known that
the standard deviation of all such fills is equal to σ = 0.2 ounces. It is desired to estimate the true mean
fill of all cups using 99% confidence.
A. Should a z-statistic or a t-statistic be used to solve this problem? Explain why. (5)
B. Estimate the desired mean using 99% confidence. Should the fan take the results to the press? (12)
C. Explain in terms of this problem when the procedure used in part B is valid. (3)
D. How many cups should be sampled to estimate the desired mean to within a margin of error of 0.03
ounces using a 99% confidence interval? (9)
3. The owner of a department store randomly samples 100 customers of the store over the course of a
year, and calculates a 90% confidence interval for the average age of all customers as (18.7, 25.9). The
correct explanation for the meaning of “90% confidence” is: (circle the correct choice) (5)
A. The true mean age of all customers of the store is between 18.7 and 25.9 years of age.
B. 90% of all customers of the store are between 18.7 and 25.9 years of age.
C. 90% of the time, the mean age of all customers of the store is between 18.7 and 25.9 years old.
D. If many different samples of 100 customers of the store each were collected, and a confidence
interval constructed for each sample, then 90% of all the confidence intervals would contain the true
average age of all customers of the store.
4. A large academic institution wants to compare the grade distributions of two of its largest departments
(to avoid unnecessary angst, call them Dept.A and Dept.B). Twelve semesters are randomly sampled
over the past 30 years, and the average GPA from each department are obtained. It is desired to
estimate the difference in the mean GPA of the two departments using 95% confidence.
A. Are these two samples of GPA data independent or dependent? Explain why. (5)
B. Use the appropriate output from the STATCRUNCH ANALYSES FOR PROBLEM 4 to help estimate
the desired mean using 95% confidence. (12)
5. Harper’s Index found that 20% of American men admit they wear uncomfortable shoes because they
look good. This year, after a major advertising campaign against uncomfortable shoes by the Surgeon
General, we believe the proportion should be lower. A random sample of 70 American men is selected
and it is found that 12 admit to wearing uncomfortable shoes because they look good. Does this
indicate that the true proportion has decreased? Use α = 0.05. (15)
6. A small town administration in Ireland claims that dioxin exposure of its citizens meets federally
mandated levels. A group of citizens believes the true exposure for residents exceeds mandated levels.
A sample of the milk from 40 cows was randomly selected and the sample mean was calculated to be
x  138 , versus the EU limit of 135 units for dioxins in milk and milk products. A hypothesis test using
the hypotheses
H0: μ = 135
Ha: μ > 135
produces a p-value of 0.03. The p-value of 0.03 means: (Circle the letter of the correct response) (5)
A. If the null hypothesis is true (the mean number of units of dioxin is 135), then the probability that the
observed value of the mean of a random sample the milk of 40 cows would be x  138 , or larger, equals
0.03.
B. The probability that the null hypothesis (μ = 135) is false, and the alternative hypothesis (μ > 135) is
true is 0.03.
C. If many different samples of 40 milk samples were collected, then 3% of all such samples would
produce a sample mean of x  138 , or larger.
D. The null hypothesis is true 97% of the time.
7. The mean ozone level in San Diego was thought to exceed acceptable levels of .05 ppm. A random
sample of 69 daily ozone values were collected and their mean calculated ( x  .057, s  .020 ). Do these
data provide sufficient evidence to conclude that the mean ozone level is above the allowable limit? Use
  .01.
A. Should a z-statistic or a t-statistic be used to solve this problem? Explain why. (5)
B. Refer to STATCRUNCH ANALYSES FOR PROBLEM 7 to help determine whether there is sufficient
evidence to conclude that the mean ozone level is above the allowable limit using   .01. (12)
8. Young and Winn (2003) counted sightings of the spotted moray eel, Gymnothorax moringa, and the
purplemouth moray eel, G. vicinus, in a 150-m by 250-m area of reef in Belize. They identified each eel
they saw, and classified the locations of the sightings into three types: those in grass beds, those in
sand and rubble, and those within one meter of the border between grass and sand/rubble. The number
of sightings are shown in the table, with percentages in parentheses:
G. moringa
G. vicinus
Grass
127 (25.4)
116 (33.7)
Sand
99 (19.8)
67 (19.5)
Border
274 (54.8)
161 (46.8)
The nominal variables are the species of eel (G. moringa or G. vicinus and the habitat type (grass, sand, or
border). Refer to STATCRUNCH ANALYSES FOR PROBLEM 8 to help answer the following.
A. Do the data present sufficient evidence to indicate that whether eel sightings depends upon their
location? Test using α = .05. (12)
B. Based on the analysis, and provided we have evidence to reject independence between sightings
and location, explain the meanings of the percentages of eel sightings by location. (5)
C. What can we conclude about the eels and their preferences for location? (5)
9. The presence of harmful insects in farm fields is detected by erecting boards covered wtih a sticky
material and then examining the insects trapped on the board. Which colors are most attractive to cereal
leaf beetles? 6 boards in 4 colors were placed in a field of oats. Refer to STATCRUNCH ANALYSES
FOR PROBLEM 9 to help answer the following. Conduct all analyses using α =.05.
A. Do the data provide sufficient evidence at the level that the leaf beetles have different mean
attractions to the colors? (12)
B. If appropriate, determine which colors have significantly different attractivity to the beetles. Conduct
all tests at a .05 level of significance. (12)
10. Pierce (1949) measured the frequency (the number of wing vibrations per second) of chirps made by
a ground cricket, at various ground temperatures. Since crickets are ectotherms (cold-blooded), the rate
of their physiological processes and their overall metabolism are influenced by temperature.
Consequently, there is reason to believe that temperature would have a profound effect on aspects of
their behavior, such as chirp frequency.
It is desired to investigate the relationship between chirp rate and temperature. A random sample of 15
pairs of chirp rates and temperatures were recorded. Refer to STATCRUNCH ANALYSES FOR
PROBLEM 10 to help answer the following.
A. Is there sufficient evidence to conclude that chirp rates are correlated with temperature? Use a .05
level of significance. (12)
B. Interpret the value of the slope in terms of this scenario. (4)
C. If appropriate, estimate the chirp rate for a cricket at 72 degrees, using 95% confidence. If not
appropriate, explain why. (6)
D. If appropriate, estimate the mean chirp rate for all crickets at 72 degrees using 95% confidence. If
not appropriate, explain why. (6)
E. Interpret the strength of the linear relationship between city and highway gas mileages. (6)