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Statistics
7.3 Review
Name _____________________
Date ______
Directions: Complete ALL of the following problems. Use the formulas
provided or your calculator program(s).
𝜎
𝑠
𝑥̅ − 𝐸 < 𝜇 < 𝑥̅ + 𝐸
𝐸 = 𝑧𝛼 • 𝑛
𝐸 = 𝑡𝛼 • 𝑛
√
2
2
𝑍𝛼 • 𝜎
𝑛=[
2
𝐸
2
√
]
1. A coffee vending machine fills 100 cups of coffee before it has to be refilled. On Monday
the mean number of ounces in a filled cup of coffee was 7.35. The population standard
deviation is known to be 0.25 ounces. Find the 95% confidence interval for the mean number
of ounces of coffee dispensed by this machine. What is unrealistic about this problem?
2. A Gallup poll conducted December 20-21, 1999, asked 1031 randomly selected Americans,
“How often do you bathe each week? Results of the survey indicated that 𝑥̅ = 6.9
and 𝑠 = 2.8. Construct a 99% confidence interval for the number of times Americans bathed
each week in 1999. Interpret the interval.
3. A survey of hospital records of 25 randomly selected patients suffering from a particular
disease indicated that the average length of stay in the hospital is 10 days. The standard
deviation is estimated to be 2.1 days and the distribution is known to be normal. Find a 99%
confidence interval for estimating the mean length of stay in the hospital.
4. Suppose we wish to estimate the average life of a calculator to within 0.75 years of the true
value. Past experience indicates that the standard deviation is 2.6 years. How large a
sample must be selected if we want our answer to be within 0.75 years 95% of the time?
5. Tim Kelley has been weighing himself once a week for several years. Last month his four
measurements (𝑖𝑛 𝑝𝑜𝑢𝑛𝑑𝑠) were
190.5
189.0
195.5
187.0
Give a 90% confidence interval for his mean weight for last month and interpret the
results. Assume that the distribution of this data is normal.
6. How do you determine whether to use the 𝑧 or 𝑡 distribution?
7. One of the important factors in auto safety is the weight of the vehicle. Insurance
companies are interested in knowing the average weight of cars currently licensed in the
United States; they believe it is 3000 pounds. To see if that estimate is correct, they
checked a random sample of 91 cars. From that group the mean weight was 2919 pounds,
with a standard deviation of 531.5 pounds. Find a 95% confidence level estimate of the
population mean. Is there strong evidence that the mean weight of all cars is not 3000
pounds? Why or why not?