Download STAT 110 - Homework #4 (20 pts

STAT 110 - Homework #7 (38 pts.) (DUE SUNDAY, OCTOBER 11th)
1.) The admissions office claims that the mean cost of books for students at Winona
State University is $250.00 per semester. Based on data that was collected by one of my
statistics courses a few years ago we have the following summary information regarding
the cost of books for students per semester.
Sample Mean
x  269.3389
Sample Std Dev
s = 91.9895
Sample Size
n = 239
a) Do these data provide sufficient evidence that the mean cost of books for students per
semester at WSU exceeds $250.00? Be sure to justify your conclusion and show all your
work! (4 pts.)
b) Construct and interpret a 95% CI for the mean book cost per semester for WSU
students. (4 pts.)
2.) Hypertension is defined as a blood pressure over 140 mmHg systolic and/or over 90
mmHg diastolic. Hypertension, if not corrected, can cause long-term health problems. In
the college-age population (18-24 years of age), about 9.2% have hypertension. Suppose
that a blood donor program is occurring in a college dormitory during finals week.
Before each student gives blood, the nurse takes a blood pressure reading. Of 196
donors, it was found that 29 have hypertension. Do these data indicate that the
population proportion of students with hypertension during final exams week is higher
than 9.2%? Justify your answer. (4 pts.)
3.) A study of 200 rainbow trout that were caught on a baited barbed hook and then
released with the line cut at the hook (but the hook not removed from the fish) showed
that 58 fish died. Find and interpret a 95% confidence interval for the proportion of all
rainbow trout that die when caught and released using the described method. (4 pts.)
4.) In 1960, census results indicated that the age at which American men first married
had a mean of 23.3 years. It is widely suspected that young people today are waiting
longer to get married. Investigators wanted to find out if the mean age of first marriage
has increased during the past 40 years. A sample of n = 40 men who married for the first
time last year was taken. The men in this sample married at an average age of 24.2 years
with a standard deviation of 5.3 years. Is there evidence the mean age that men are first
getting married has increased when compared to the 1960 figure? (4 pts.)
5.) In a paper in the Applied Psycholinguistics (June, 1998) researchers reported on a
study of language skills of low-income children. In one part of the study researchers
administered the Communicative Development Inventory (CDI) exam to a sample of 65
low-income children. The sentence complexity scores had a mean of 7.62 and a standard
deviation of 8.91.
a)
Construct and interpret a 90% confidence interval for the mean sentence
complexity score of all low-income children. (4 pts.)
b) Suppose we know that the true mean sentence complexity score of middle-income
children is 15.55. Is there evidence that the true mean for low-income children differs
from 15.55? Explain using your answer from part (a). (2 pts.)
6.) The “fear of negative evaluation” (FNE) scores for 11 bulimic female students and 14
normal female students are presented below. Enter these data into JMP using a separate
column for each sample. Copy and paste your JMP output into your assignment.
Bulimic 21 13 10 20 25 19 16 21
Normal
a)
13 6
16 13
8
24 13 14
19 23 18 11
19
7 10 15 20
Construct a 95% confidence interval for the mean FNE score of the population of
bulimic female students. (3 pts.)
b) Construct a 95% confidence interval for the mean FNE score of the population of
normal female students. (3 pts.)
c)
What must we assume about the FNE scores for these two populations? Are these
assumptions reasonable satisfied? Explain. (2 pts.)
Determining Sample Sizes
7.) A gigantic warehouse located in Tampa, FL stores approximately 60 million empty
aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke
from the fire contaminated many of the cans with blackspot, rendering them unusable. A
University of South Florida statistician was hired by the insurance company to estimate,
p, the true proportion of cans in the warehouse that were contaminated by the fire. How
many aluminum cans should be randomly sampled to estimate the true proportion to
within .02 with 95% confidence if….
a) We assume nothing about the what the true proportion might be? (2 pts.)
b) We assume that the proportion contaminated is no less than .80 or 80%? (2 pts.)
8.) According to a Food and Drug Administration (FDA) study, a cup of coffee contains
average of 115 milligrams (mg) of caffeine, with the amount per ranging from 60 mg to
180 mg. Suppose you want to repeat the FDA experiment using cups of coffee sampled
from Mugby Junction and want to estimate the mean caffeine content correct to within 5
mg with 95% confidence. How many cups of coffee would you have to include in your
study to meet this objective? (4 pts.)