Homework #6
Due Thursday, June 17
1. In the following questions:
a) Check to see IF a confidence interval can be done (i.e. – look for problems with normality and/or
asking you to estimate the statistic rather than the parameter)
b) If it is valid, construct the CI asked for. You may either do it by hand or on the computer. IF you
do it using the computer, you must print out a copy of your output! If you do it by hand, you must
show your work.
A. We are interested in the proportion of Texas drivers that had an accident last year who own a cell
phone. In a sample of 25 drivers with accidents, it was found that 15% of them use a cellular phone.
Estimate the true proportion with a 90% confidence interval.
B. I want to know what the average amount of time a student watches TV is for all Stat 303 students. Let's
use the data that we collected at the beginning of the semester as our sample. In our sample of 75
respondents, we saw a mean of 9.52 hrs. and a standard deviation of 7.2. Construct a 95% confidence
interval for the true mean heights of the population of all Stat 303 students.
C. A nutritionist is studying the average mgs of sodium in snack foods, particularly plain potato chips.
She randomly sampled 25 one-ounce servings of plain potato chips and found an average of 155 mg of
sodium with a standard deviation of 5.2 mg. Assuming the sodium content is normally distributed what
would our 99% confidence interval be to estimate the true average sodium content in plain potato chips?
D. Suppose the same nutritionist in C decides to look at flavored potato chips. Once again she randomly
samples 25 one-ounce servings of flavored potato chips and finds an average of 161 mg of sodium with a
standard deviation of 13.3 mg. If we don't make any assumption about how the sodium is distributed, what
would our 95% confidence interval be to estimate
x
?
E. While living in Idaho, I found that everyone believes that Texans wear cowboy hats and drive trucks. I
am interested in estimating the true proportion of Aggies that drive trucks. Using your class data, I found
that in our sample of 75, 17 Aggies drove trucks. Estimate the true proportion using a 90% confidence
interval.
2. What does α mean in terms of our confidence intervals?
3. I want to find out what proportion of people who are quitting smoking have put on 10 or more pounds.
I want to estimate this using a 95% confidence interval and I want to be within say roughly 5%. What
should my sample size be?
4. For the following pairs, indicate which don't comply with our rules for setting up hypotheses, and
explain why (if they don't)
a) 15: ,15:
0=> µµ a
HH
b) 50.0: ,60.0:
0<= ππ a
HH
c) 23: ,23:
0≠=XHXHa
d) 102: ,102:
0>= µµ a
HH
5. p. 309 #9.14 and #9.16
6 . What does the level of significance, α, mean in hypothesis testing? In terms of our steps, where does it
play a major role?
