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Notes 9.3 Day 2
Name____________________
Confidence Intervals for Population Mean
Confidence Intervals with Data:
1. The following is data on the cadence (strides per second) for a sample of 20 randomly selected healthy
American men.
.95 .85 .92 .95 .93 .86 1.00 .92 .85 .81
.78 .93 .93 1.05 .93 1.06 .96
.81 .96 1.06
Construct a 99% confidence interval for  =the true mean cadence of healthy American men.
Req
Math
Conclusion
2. A new process for producing synthetic gems yielded six stones weighing 0.43 , 0.52 , 0.46 , 0.49 , 0.60 ,
and 0.56 carats respectively, in its first run. Find a 90% confidence interval estimate for the mean carat
weight from this process.
3. The following data are the calories per half-cup serving for 16 popular chocolate ice cream brands
reviewed by Consumer Reports(July 1999)
270 150 170 140 160 160 160 290
190 190 160 170 150 110 180 170
Is it reasonable to use the t confidence interval to compute a confidence interval for  , the true mean
calories per half-cup serving of chocolate ice cream? Explain why or why not.
Sample Size Questions:
4. Ball bearings are manufactured by a process that results in a standard deviation in diameter of 0.025 inch.
What sample size should be chosen if we wish to be 99% sure of knowing the diameter to within 0.01 inch.
5. Sierra College wants to estimate the mean costs of text books per quarter. For it to be useful it has to be
within $20. How large a sample should be selected? S C estimates that each student spends between $450
and $50.
You Try:
6. A bottling machine is operating with a standard deviation of 0.12 ounce. Suppose that in an SRS of 36
bottles the machine inserted an average of 16.1 ounces into each bottle.
Estimate the mean number of ounces in all the bottles this machine fills.
7. A manufacturing of college textbooks is interested in estimating the strength of the bindings produced by a
particular binding machine. Strength can be measured by recording the force required to pull the pages
from the binding. If this force is measured in pounds, how many books should be tested to estimate with
95% confidence to within 0.1 lb, the average force required to break the binding? Assume that  is known
to be 0.8 lb.
8. The Degree of Reading Power (DRP) is a test of the reading ability of children. Here are DRP scores for a
sample of 44 third grade students in a suburban school district:
40 26 39 14 42 18 25 43 46 27 19 47 19 26 35 34 15 44 40 38 31 46
52 25 35 35 33 29 34 41 49 28 52 47 35 48 22 33 41 51 27 14 54 45
a. Give a 99% confidence interval for the mean score in the district.
b. Would you trust your conclusion from part A if these scores came from a single class in one school in the
district? Why?