AP Statistics
UNIT 4 - Chapter 10 HOMEWORK
Name______________________________
Date _______________
1) Bottles of a popular soda are supposed to contain 300 milliliters of cola. There
is some variation from bottle to bottle because the filling machinery is not
perfectly precise. The distribution of the contents is normal with standard
deviation  = 3 ml. An inspector who suspects that the bottler is underfilling
measures the contents of 6 bottles. The results are:
299.4
297.7
301.0
298.9
300.2
297.0
Is this convincing evidence that the mean contents of cola bottle is less than the
advertised 300 ml?
2) Radon is a colorless, odorless gas that is naturally released by rocks and soils
and may concentrate in tightly closed houses. Because radon is slightly radioactive,
there is some concern that it may be a health hazard. Radon detectors are sold to
homeowners worried about this risk, but the detectors may be inaccurate.
University researchers placed 12 detectors in a chamber where they were exposed
to 105 picocuries per liter of radon over 3 days. Here are the readings given by the
detectors:
91.9
103.8
97.8
99.6
111.4
96.6
122.3
119.3
105.4
104.8
95.0
101.7
Assume (unrealistically) that you know that the standard deviation of readings for
all the detectors of this type is  = 9.
a) Give a 90% confidence interval for the mean reading  for this type of
detector.
b) Is there significant evidence at the 10% level that the mean reading
differs from the true value 105? State hypotheses and base a test on
your confidence interval from part a.
3) The high temperature in Chicago for the month of August is distributed
approximately normally with mean  = 80 degrees and  = 8 degrees. A random
sample of 10 days in Chicago during August 2000 results in the following data.
77
81
72
86
76
81
73
92
75
97
a) Construct a 95% confidence interval for the mean temperature in August
in Chicago. Interpret this interval. Check with a calculator.
b) Is there evidence that the mean temperature for August 2000 is
different from the mean? Test at 5%.
4) A Gallup poll conducted in 1999 asked Americans how many hours of TV they
watched during the week. How many subjects would be needed in order to estimate
the mean within .5 hours (MOE) with 95% confidence? Assume  = 1.8.
5) In 1990 the average farm size in Kansas was 694 acres, according to data
obtained from the US Department of Agriculture. A researcher claims that farm
sizes are larger now due to consolidation of farms. She obtains a SRS of 40 farms
and determines the mean to be 731 acres. Assume that  = 212 acres. Test the
researchers claim at the 5% level.
6) The average daily volume of Motorola sock in 2000 was  = 31.8 million shares
with a standard deviation of  = 8.3 million shares. A stock analyst claims that the
stock volume in 2001 is different from the 2000 level. Based on a SRS of 35
trading days in 2001, he finds the sample mean to be 15 million shares. Test the
claim at the 5% level.