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AP Statistics
Mixed Review Inference on Means Activity
1) The Environmental Protection Agency sets limits on the maximum allowable concentration of certain
chemicals in drinking water. For the substance PCB, the limit was been set at 5 ppm (parts per million). A
random sample of 36 water specimens from the same well results in a mean PCB concentration of 5.2 ppm
with standard deviation of 0.6 ppm. Does the data substantiate that the water is unsafe at the .01 significance
level?
2) Identify the type I & II errors for the hypotheses in question 1. State a consequence for each.
3) Suppose the red blood cell count (RBC) in millions per cubic millimeter of whole blood for healthy
female adults is normally distributed with a mean of 4.8 and standard deviation of 0.4. A female patient has
taken six blood tests over the past several months with a mean of 4.47. What is a 95% confidence interval
for this patient’s true mean RBC? Based upon this interval, does this indicate that her RBC is lower than the
population mean?
4) The Wall Street Journal stated that the cost to repair a vacuum cleaner was $54, nationally. In a random
sample of 25 vacuum repair jobs in Plano, the mean repair cost was $56.29 with a standard deviation of
$6.41. Assume repair costs are normally distributed. Does this indicate the he cost of vacuum repair in
Plano is higher than the national average?
5) In Secrets of Sleep, by Professor Borbely, a random sample of 38 college students was kept awake for 24
hours. The mean time for this group to go to sleep the next night was 2.5 minutes with a standard deviation
of 0.7 minutes. Compute a 90% confidence interval for the mean time of all such sleep-deprived students to
fall asleep.
6) Consumer Reports gave the following data about the life (in hours) of AA Duracell batteries for a certain
toy. Compute a 98% confidence interval for the mean life of AA Duracell batteries for that toy.
2.3
2.5
4.2
6.1
5.7
5.5
1.3
1.5
5.4
5.3
1.8
1.9
5.2
1.8
5.1
7) Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known to
contain an average of 6.9 new words (words not used in the poet’s other works). Assume the distribution of
new words is normally distributed with standard deviation of 2.7 words. Now a manuscript with 5 new
sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain
an average of 8.2 words not used in the poet’s known works. We expect poems by another author to contain
more new words. Is there sufficient evidence to suggest that this manuscript is by another author?
8) To assess the impact of quality circles (groups of employees who meet to discuss issues related to product
quality) on employee job satisfaction, 73 employees who participated in quality circles were studied.
Suppose that the mean score for job satisfaction for all employees is 3.12. The mean job satisfaction for the
sample is 3.18 with standard deviation of .99. Is the mean job satisfaction for employees participating in
quality circles higher than the general working population? (α = .10)